View allAll Photos Tagged polynomials
SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 1920 / length of data axis 1
NAXIS2 = 1080 / length of data axis 2
NAXIS3 = 3 / length of data axis 3
EXTEND = T / FITS dataset may contain extensions
COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy
COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H
BZERO = 0. / Offset data range to that of unsigned short
BSCALE = 1. / Default scaling factor
PROGRAM = 'Siril 1.4.0-beta2' / Software that created this HDU
FILENAME= 'Light_M 56_20.0s_IRCUT_20250620-022630.fit'
DATE = '2025-06-20T16:37:26' / UTC date that FITS file was created
DATE-OBS= '2025-06-20T07:26:05.200059' / YYYY-MM-DDThh🇲🇲ss observation start,
IMAGETYP= 'Light ' / Type of image
ROWORDER= 'BOTTOM-UP' / Order of the rows in image array
EXPTIME = 20. / [s] Exposure time duration
TELESCOP= 'S50_f1c10930' / Telescope used to acquire this image
FILTER = 'mixed ' / Active filter name
APERTURE= 5. / Aperture of the instrument
FOCALLEN= 251.96 / [mm] Focal length
XBINNING= 1 / Camera binning mode
YBINNING= 1 / Camera binning mode
XPIXSZ = 2.90000009536743 / [um] Pixel X axis size
YPIXSZ = 2.90000009536743 / [um] Pixel Y axis size
INSTRUME= 'Seestar S50' / Instrument name
CCD-TEMP= 27.3125 / [degC] CCD temperature
GAIN = 80 / Sensor gain
FOCPOS = 1613 / [step] Focuser position
STACKCNT= 206 / Stack frames
LIVETIME= 4120. / [s] Exposure time after deadtime correction
EXPSTART= 2460846.73287569 / [JD] Exposure start time (standard Julian date)
EXPEND = 2460846.81181769 / [JD] Exposure end time (standard Julian date)
OBJECT = 'M 56 ' / Name of the object of interest
SITELAT = 41.7559 / [deg] Observation site latitude
SITELONG= -88.1817 / [deg] Observation site longitude
OBJCTRA = '19 16 26.982' / [H M S] Image center Right Ascension
OBJCTDEC= '+30 12 13.731' / [D M S] Image center Declination
RA = 289.112423089719 / [deg] Image center Right Ascension
DEC = 30.2038140437823 / [deg] Image center Declination
CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions
CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions
CUNIT1 = 'deg ' / Unit of coordinates
CUNIT2 = 'deg ' / Unit of coordinates
EQUINOX = 2000. / Equatorial equinox
CRPIX1 = 960.5 / Axis1 reference pixel
CRPIX2 = 540.5 / Axis2 reference pixel
CRVAL1 = 289.112423089719 / [deg] Axis1 reference value
CRVAL2 = 30.2038140437823 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000659417750777937 / [deg] X pixel size
CDELT2 = 0.000659504173170408 / [deg] Y pixel size
PC1_1 = 0.0180150755877486 / Linear transformation matrix (1, 1)
PC1_2 = -0.999837715357631 / Linear transformation matrix (1, 2)
PC2_1 = 0.999838194893443 / Linear transformation matrix (2, 1)
PC2_2 = 0.0179884416284617 / Linear transformation matrix (2, 2)
A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky
A_0_0 = 0.
A_1_0 = 0.
A_0_1 = 0.
A_2_0 = -3.06754913775013E-08
A_1_1 = 1.89953693775213E-07
A_0_2 = -1.22525701990691E-08
A_3_0 = 1.82746303654987E-11
A_2_1 = -2.37472860590852E-11
A_1_2 = -6.44280581301157E-11
A_0_3 = 9.15603245331978E-11
B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky
B_0_0 = 0.
B_1_0 = 0.
B_0_1 = 0.
B_2_0 = 3.73073190900284E-09
B_1_1 = 6.12634206923396E-08
B_0_2 = 3.0295880067713E-07
B_3_0 = -1.22087818507584E-11
B_2_1 = -6.18980783966298E-13
B_1_2 = -2.01897390555819E-12
B_0_3 = -1.61168371273834E-10
AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = 6.30062773521541E-07
AP_1_0 = 7.77813369268188E-11
AP_0_1 = 1.20700416279107E-10
AP_2_0 = 3.06674409261316E-08
AP_1_1 = -1.89961587190837E-07
AP_0_2 = 1.22759422132304E-08
AP_3_0 = -1.82713777563363E-11
AP_2_1 = 2.37438507398206E-11
AP_1_2 = 6.45222698000841E-11
AP_0_3 = -9.1583509422043E-11
BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = 2.75600846753354E-06
BP_1_0 = -6.10953113260446E-10
BP_0_1 = -1.86755522157966E-09
BP_2_0 = -3.73080388499817E-09
BP_1_1 = -6.12834284817647E-08
BP_0_2 = -3.0303462111585E-07
BP_3_0 = 1.22090606994075E-11
BP_2_1 = 6.24774656346552E-13
BP_1_2 = 2.09264856534272E-12
BP_0_3 = 1.61379454454441E-10
CREATOR = 'ZWO Seestar S50' / Capture software
PRODUCER= 'ZWO ' / Powered by ZWO
XORGSUBF= 0 / Subframe X position in binned pixels
YORGSUBF= 0 / Subframe Y position in binned pixels
EQMODE = 1 / Equatorial mode
CCDXBIN = 1 / Camera X Bin
CCDYBIN = 1 / Camera Y Bin
TOTALEXP= 20. / Total Exposure Time in seconds
BG-EXTR = 'GraXpert'
CBG-1 = 0.0044073015
CBG-2 = 0.0044073015
CBG-3 = 0.0044073015
INTP-OPT= 'RBF '
HIERARCH SMOOTHING = 0.5
HIERARCH CORR-TYPE = 'Subtraction'
HIERARCH SAMPLE-SIZE = 15
HIERARCH RBF-KERNEL = 'thin_plate'
HIERARCH SPLINE-ORDER = 3
BG-PTS = '[[555, 9, 1], [627, 9, 1], [699, 9, 1], [741, 9, 1], [813, 9, 1], &'
CONTINUE '[411, 111, 1], [555, 111, 1], [627, 111, 1], [699, 111, 1], [771, &'
CONTINUE '111, 1], [813, 111, 1], [885, 111, 1], [339, 183, 1], [381, 183, &'
CONTINUE '1], [453, 183, 1], [525, 183, 1], [597, 183, 1], [699, 183, 1], &'
CONTINUE '[771, 183, 1], [843, 153, 1], [885, 183, 1], [987, 183, 1], [1029, &'
CONTINUE '183, 1], [267, 255, 1], [339, 255, 1], [396, 240, 1], [453, 255, &'
CONTINUE '1], [525, 255, 1], [597, 255, 1], [699, 255, 1], [771, 225, 1], &'
CONTINUE '[828, 240, 1], [885, 255, 1], [987, 255, 1], [1044, 240, 1], [195, &'
CONTINUE '297, 1], [267, 327, 1], [324, 312, 1], [396, 312, 1], [453, 327, &'
CONTINUE '1], [540, 312, 1], [597, 297, 1], [699, 327, 1], [771, 297, 1], &'
CONTINUE '[843, 297, 1], [915, 327, 1], [972, 312, 1], [1029, 327, 1], [195, &'
CONTINUE '399, 1], [237, 399, 1], [309, 369, 1], [381, 399, 1], [453, 399, &'
CONTINUE '1], [555, 369, 1], [597, 399, 1], [699, 369, 1], [756, 384, 1], &'
CONTINUE '[843, 399, 1], [915, 399, 1], [987, 369, 1], [1059, 399, 1], [21, &'
CONTINUE '471, 1], [108, 456, 1], [195, 471, 1], [267, 471, 1], [339, 471, &'
CONTINUE '1], [381, 471, 1], [483, 441, 1], [525, 471, 1], [627, 441, 1], &'
CONTINUE '[699, 471, 1], [771, 471, 1], [813, 441, 1], [915, 471, 1], [987, &'
CONTINUE '441, 1], [1029, 471, 1], [21, 543, 1], [93, 543, 1], [195, 543, &'
CONTINUE '1], [237, 543, 1], [339, 543, 1], [381, 543, 1], [453, 543, 1], &'
CONTINUE '[555, 543, 1], [627, 543, 1], [699, 543, 1], [741, 543, 1], [843, &'
CONTINUE '513, 1], [915, 513, 1], [957, 543, 1], [1059, 543, 1], [51, 615, &'
CONTINUE '1], [123, 615, 1], [165, 585, 1], [237, 585, 1], [324, 600, 1], &'
CONTINUE '[381, 615, 1], [453, 615, 1], [555, 615, 1], [597, 615, 1], [699, &'
CONTINUE '615, 1], [771, 615, 1], [843, 615, 1], [915, 585, 1], [987, 615, &'
CONTINUE '1], [1059, 615, 1], [51, 687, 1], [93, 687, 1], [195, 687, 1], &'
CONTINUE '[267, 687, 1], [309, 657, 1], [396, 672, 1], [453, 657, 1], [525, &'
CONTINUE '687, 1], [597, 657, 1], [699, 687, 1], [771, 657, 1], [843, 687, &'
CONTINUE '1], [779.7394136807818, 704.6254071661238, 1.0], [987, 657, 1], &'
CONTINUE '[1029, 687, 1], [21, 729, 1], [123, 759, 1], [180, 744, 1], [267, &'
CONTINUE '759, 1], [324, 744, 1], [396, 744, 1], [453, 729, 1], &'
CONTINUE '[484.75570032573296, 729.6416938110749, 1.0], [627, 729, 1], [699, &'
CONTINUE '729, 1], [771, 759, 1], [843, 729, 1], [855.830618892508, &'
CONTINUE '766.1237785016286, 1.0], [972, 744, 1], [1029, 759, 1], [51, 831, &'
CONTINUE '1], [123, 831, 1], [165, 831, 1], [267, 831, 1], [309, 801, 1], &'
CONTINUE '[396, 816, 1], [453, 801, 1], [573.3550488599349, &'
CONTINUE '721.3029315960912, 1.0], [655.700325732899, 673.3550488599349, &'
CONTINUE '1.0], [899.6091205211728, 690.0325732899023, 1.0], [741, 801, 1], &'
CONTINUE '[813, 831, 1], [915, 801, 1], [987, 831, 1], [1059, 801, 1], [51, &'
CONTINUE '873, 1], [123, 873, 1], [195, 873, 1], [267, 873, 1], [309, 873, &'
CONTINUE '1], [381, 873, 1], [316.9381107491856, 833.8762214983714, 1.0], &'
CONTINUE '[733.8762214983715, 854.7231270358307, 1.0], [774.5276872964168, &'
CONTINUE '855.7654723127035, 1.0], [771, 903, 1], [813, 903, 1], [915, 873, &'
CONTINUE '1], [972, 888, 1], [1059, 903, 1], [51, 945, 1], [123, 945, 1], &'
CONTINUE '[165, 945, 1], [252, 960, 1], [309, 945, 1], [381, 945, 1], &'
CONTINUE '[364.88599348534194, 994.3973941368079, 1.0], [768.2736156351793, &'
CONTINUE '1013.1596091205212, 1.0], [771, 945, 1], [843, 975, 1], [885, 975, &'
CONTINUE '1], [972, 960, 1], [1059, 975, 1], [51, 1047, 1], [123, 1017, 1], &'
CONTINUE '[165, 1017, 1], [237, 1047, 1], [309, 1017, 1], [381, 1047, 1], &'
CONTINUE '[565.0162866449512, 1220.586319218241, 1.0], [660.9120521172638, &'
CONTINUE '1122.6058631921824, 1.0], [750.5537459283387, 1048.599348534202, &'
CONTINUE '1.0], [771, 1047, 1], [813, 1017, 1], [885, 1017, 1], [972, 1032, &'
CONTINUE '1], [1029, 1017, 1], [51, 1119, 1], [123, 1089, 1], [165, 1119, &'
CONTINUE '1], [252, 1104, 1], [309, 1089, 1], [396, 1104, 1], &'
CONTINUE '[384.69055374592836, 1185.1465798045601, 1.0], [522.2801302931596, &'
CONTINUE '1217.459283387622, 1.0], [627, 1119, 1], [699, 1119, 1], [741, &'
CONTINUE '1089, 1], [843, 1089, 1], [885, 1089, 1], [957, 1119, 1], [1029, &'
CONTINUE '1119, 1], [51, 1161, 1], [123, 1191, 1], [165, 1191, 1], [267, &'
CONTINUE '1191, 1], [309, 1161, 1], [381, 1191, 1], [453, 1161, 1], [525, &'
CONTINUE '1161, 1], [627, 1191, 1], [699, 1161, 1], [741, 1161, 1], [813, &'
CONTINUE '1161, 1], [885, 1161, 1], [972, 1176, 1], [1029, 1191, 1], [51, &'
CONTINUE '1233, 1], [108, 1248, 1], [195, 1233, 1], [267, 1233, 1], [339, &'
CONTINUE '1233, 1], [396, 1248, 1], [453, 1233, 1], [525, 1233, 1], [627, &'
CONTINUE '1233, 1], [699, 1233, 1], [771, 1263, 1], [813, 1233, 1], [915, &'
CONTINUE '1233, 1], [957, 1233, 1], [1029, 1263, 1], [51, 1335, 1], [108, &'
CONTINUE '1320, 1], [195, 1305, 1], [237, 1305, 1], [324, 1320, 1], [381, &'
CONTINUE '1335, 1], [483, 1335, 1], [540, 1320, 1], [627, 1305, 1], [699, &'
CONTINUE '1305, 1], [771, 1335, 1], [813, 1335, 1], [915, 1335, 1], [957, &'
CONTINUE '1335, 1], [1059, 1335, 1], [36, 1392, 1], [93, 1377, 1], [165, &'
CONTINUE '1377, 1], [267, 1377, 1], [309, 1377, 1], [381, 1407, 1], [483, &'
CONTINUE '1407, 1], [555, 1407, 1], [627, 1407, 1], [699, 1377, 1], [741, &'
CONTINUE '1407, 1], [813, 1407, 1], [885, 1407, 1], [987, 1407, 1], [1029, &'
CONTINUE '1407, 1], [51, 1449, 1], [93, 1449, 1], [267, 1449, 1], [309, &'
CONTINUE '1449, 1], [411, 1479, 1], [483, 1449, 1], [555, 1479, 1], [627, &'
CONTINUE '1479, 1], [699, 1479, 1], [771, 1479, 1], [843, 1479, 1], [915, &'
CONTINUE '1479, 1], [987, 1479, 1], [1059, 1449, 1], [36, 1536, 1], [93, &'
CONTINUE '1521, 1], [165, 1551, 1], [237, 1551, 1], [339, 1521, 1], [381, &'
CONTINUE '1551, 1], [483, 1521, 1], [555, 1521, 1], [627, 1521, 1], [684, &'
CONTINUE '1536, 1], [771, 1551, 1], [843, 1551, 1], [885, 1521, 1], [987, &'
CONTINUE '1551, 1], [1029, 1521, 1], [51, 1623, 1], [93, 1593, 1], [195, &'
CONTINUE '1593, 1], [237, 1623, 1], [309, 1623, 1], [411, 1623, 1], [453, &'
CONTINUE '1623, 1], [525, 1623, 1], [627, 1623, 1], [699, 1623, 1], [771, &'
CONTINUE '1623, 1], [843, 1593, 1], [915, 1623, 1], [987, 1623, 1], [1029, &'
CONTINUE '1593, 1], [51, 1695, 1], [123, 1665, 1], [195, 1665, 1], [267, &'
CONTINUE '1665, 1], [339, 1695, 1], [411, 1695, 1], [483, 1695, 1], [555, &'
CONTINUE '1695, 1], [627, 1695, 1], [699, 1665, 1], [771, 1695, 1], [843, &'
CONTINUE '1695, 1], [915, 1695, 1], [987, 1695, 1], [1029, 1695, 1], [21, &'
CONTINUE '1767, 1], [108, 1752, 1], [165, 1767, 1], [267, 1767, 1], [309, &'
CONTINUE '1767, 1], [396, 1752, 1], [483, 1737, 1], [555, 1767, 1], [627, &'
CONTINUE '1767, 1], [699, 1767, 1], [771, 1767, 1], [843, 1767, 1], [915, &'
CONTINUE '1767, 1], [987, 1767, 1], [1029, 1767, 1], [21, 1839, 1], [93, &'
CONTINUE '1839, 1], [165, 1839, 1], [252, 1824, 1], [339, 1809, 1], [411, &'
CONTINUE '1839, 1], [483, 1839, 1], [555, 1839, 1], [627, 1809, 1], [699, &'
CONTINUE '1809, 1], [771, 1839, 1], [843, 1809, 1], [915, 1839, 1], [987, &'
CONTINUE '1839, 1], [1059, 1839, 1], [21, 1911, 1], [93, 1881, 1], [165, &'
CONTINUE '1911, 1], [267, 1881, 1], [309, 1881, 1], [411, 1881, 1], [483, &'
CONTINUE '1881, 1], [555, 1881, 1], [627, 1881, 1], [699, 1911, 1], [771, &'
CONTINUE '1911, 1], [843, 1911, 1], [915, 1911, 1], [987, 1911, 1], [1059, &'
CONTINUE '1911, 1], [32, 322, 1], [51, 339, 1], [123, 309, 1], [36, 396, 1], &'
CONTINUE '[123, 411, 1], [123, 267, 1], [53, 93, 1], [93, 51, 1], [180, 36, &'
CONTINUE '1], [51, 93, 1], [108, 108, 1], [195, 123, 1], [21, 165, 1], [123, &'
CONTINUE '165, 1], [74, 290, 1], [51, 267, 1], [214, 202, 1], [267, 195, 1], &'
CONTINUE '[321, 48, 1], [309, 51, 1], [411, 51, 1], [483, 51, 1], [267, 93, &'
CONTINUE '1], [917, 48, 1], [885, 51, 1], [987, 21, 1], [1044, 36, 1], &'
CONTINUE '[1029, 123, 1], [926, 106, 1], [927, 213, 1], [741, 339, 1], [456, &'
CONTINUE '1570, 1], [339, 1563, 1], [195, 1491, 1], [237, 1491, 1], [495, &'
CONTINUE '1570, 1], [568, 1559, 1]]'
END
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Snow Created Ice Cream Sandwich Car Art which created Mandelbrot fractal edges as it melted naturally. It seems like you might be referring to the **Mandelbrot set**, which is associated with fractal mathematics. The Mandelbrot set is defined by the complex quadratic polynomial:
\[
z_{n+1} = z_n^2 + c
\]
where:
- \( z_n \) is a complex number (initially \( z_0 = 0 \))
- \( c \) is a complex parameter
The set comprises all complex numbers \( c \) for which the sequence does not diverge to infinity. Generally, we assess the behavior of the sequence over multiple iterations to determine membership in the Mandelbrot set.
Details about Mandelbrot set is from Google's ChatGPT Sidebar GPT-4o, Claude.
Text says: "Other questions with same solution:
(1) Find the solutions to the equation z^5=(2, 35 degrees).
(2) Find the roots of the polynomial z^5-(2, 35 degrees)."
Being in one of the low level math classes not only helps me to learn polynomials, but also provides me with time to draw shit all over my papers.
SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 960 / length of data axis 1
NAXIS2 = 1733 / length of data axis 2
NAXIS3 = 3 / length of data axis 3
EXTEND = T / FITS dataset may contain extensions
COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy
COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H
BZERO = 0. / Offset data range to that of unsigned short
BSCALE = 1. / Default scaling factor
MIPS-HI = 65535 / Lower visualization cutoff
MIPS-LO = 4392 / Upper visualization cutoff
PROGRAM = 'Siril 1.4.0-beta2' / Software that created this HDU
FILENAME= 'Light_NGC 7023_20.0s_IRCUT_20250625-222221.fit'
DATE = '2025-06-26T16:14:03' / UTC date that FITS file was created
DATE-OBS= '2025-06-26T03:21:58.490870' / YYYY-MM-DDThh🇲🇲ss observation start,
IMAGETYP= 'Light ' / Type of image
ROWORDER= 'BOTTOM-UP' / Order of the rows in image array
EXPTIME = 20. / [s] Exposure time duration
TELESCOP= 'S50_f1c10930' / Telescope used to acquire this image
FILTER = 'mixed ' / Active filter name
APERTURE= 5. / Aperture of the instrument
FOCALLEN= 252.053 / [mm] Focal length
XBINNING= 1 / Camera binning mode
YBINNING= 1 / Camera binning mode
XPIXSZ = 2.90000009536743 / [um] Pixel X axis size
YPIXSZ = 2.90000009536743 / [um] Pixel Y axis size
INSTRUME= 'Seestar S50' / Instrument name
CCD-TEMP= 33.5 / [degC] CCD temperature
GAIN = 80 / Sensor gain
FOCPOS = 1629 / [step] Focuser position
STACKCNT= 44 / Stack frames
LIVETIME= 880. / [s] Exposure time after deadtime correction
EXPSTART= 2460821.6426436 / [JD] Exposure start time (standard Julian date)
EXPEND = 2460852.65457944 / [JD] Exposure end time (standard Julian date)
OBJECT = 'NGC 7023' / Name of the object of interest
SITELAT = 41.9317 / [deg] Observation site latitude
SITELONG= -88.6869 / [deg] Observation site longitude
OBJCTRA = '21 01 58.348' / [H M S] Image center Right Ascension
OBJCTDEC= '+68 07 52.059' / [D M S] Image center Declination
RA = 315.493118321513 / [deg] Image center Right Ascension
DEC = 68.131127500467 / [deg] Image center Declination
CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions
CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions
CUNIT1 = 'deg ' / Unit of coordinates
CUNIT2 = 'deg ' / Unit of coordinates
EQUINOX = 2000. / Equatorial equinox
CRPIX1 = 496.5 / Axis1 reference pixel
CRPIX2 = 819.5 / Axis2 reference pixel
CRVAL1 = 315.471044186353 / [deg] Axis1 reference value
CRVAL2 = 68.0991332832782 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000659353932434851 / [deg] X pixel size
CDELT2 = 0.000659080328939971 / [deg] Y pixel size
PC1_1 = 0.997302171168034 / Linear transformation matrix (1, 1)
PC1_2 = 0.0734055814194399 / Linear transformation matrix (1, 2)
PC2_1 = -0.0733545771633578 / Linear transformation matrix (2, 1)
PC2_2 = 0.997305923981797 / Linear transformation matrix (2, 2)
A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky
A_0_0 = 0.
A_1_0 = 0.
A_0_1 = 0.
A_2_0 = -3.20097849458524E-07
A_1_1 = 3.2881667772758E-08
A_0_2 = -1.10989697832774E-08
A_3_0 = -4.46796246892606E-10
A_2_1 = -1.56520840684043E-11
A_1_2 = -1.11723318665913E-10
A_0_3 = 6.50821408756037E-11
B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky
B_0_0 = 0.
B_1_0 = 0.
B_0_1 = 0.
B_2_0 = 1.29225403647357E-07
B_1_1 = -2.01687980694376E-07
B_0_2 = 3.25348431191491E-08
B_3_0 = 3.42075770198142E-10
B_2_1 = 1.65098920253431E-10
B_1_2 = 1.71157843224335E-12
B_0_3 = -7.71159261840328E-11
AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = -1.379153707401E-05
AP_1_0 = -2.44285431882929E-08
AP_0_1 = 2.81940860006873E-09
AP_2_0 = 3.20370675703584E-07
AP_1_1 = -3.29435425568357E-08
AP_0_2 = 1.11275283438192E-08
AP_3_0 = 4.47266442917117E-10
AP_2_1 = 1.55876136288333E-11
AP_1_2 = 1.11808336760055E-10
AP_0_3 = -6.51059584939392E-11
BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = 7.73895816842519E-06
BP_1_0 = 1.84455965627406E-08
BP_0_1 = 2.68261035607509E-09
BP_2_0 = -1.29380463883567E-07
BP_1_1 = 2.01738193180362E-07
BP_0_2 = -3.25630941158686E-08
BP_3_0 = -3.42382944687177E-10
BP_2_1 = -1.65040121775154E-10
BP_1_2 = -1.76837979602864E-12
BP_0_3 = 7.71327348315469E-11
HISTORY Crop (x=44, y=46, w=960, h=1733)
HISTORY Saturation enhancement (amount=0.20)
HISTORY Saturation enhancement (amount=0.13)
HISTORY Saturation enhancement (amount=0.12)
CREATOR = 'ZWO Seestar S50' / Capture software
PRODUCER= 'ZWO ' / Powered by ZWO
XORGSUBF= 0 / Subframe X position in binned pixels
YORGSUBF= 0 / Subframe Y position in binned pixels
EQMODE = 1 / Equatorial mode
CCDXBIN = 1 / Camera X Bin
CCDYBIN = 1 / Camera Y Bin
TOTALEXP= 20. / Total Exposure Time in seconds
END
Degree of polynomial In case of a polynomial involving in one variable, the highest power of the variable is called the degree of the polynomial.
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SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 2160 / length of data axis 1
NAXIS2 = 3840 / length of data axis 2
NAXIS3 = 3 / length of data axis 3
EXTEND = T / FITS dataset may contain extensions
COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy
COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H
BZERO = 0. / Offset data range to that of unsigned short
BSCALE = 1. / Default scaling factor
PROGRAM = 'Siril 1.4.0-beta1' / Software that created this HDU
DATE = '2025-05-20T09:59:58' / UTC date that FITS file was created
DATE-OBS= '2025-05-20T02:56:45.429467' / YYYY-MM-DDThh🇲🇲ss observation start,
IMAGETYP= 'Light ' / Type of image
EXPTIME = 20. / [s] Exposure time duration
TELESCOP= 'S50_83e5119e' / Telescope used to acquire this image
FILTER = 'LP ' / Active filter name
APERTURE= 5. / Aperture of the instrument
FOCALLEN= 250. / [mm] Focal length
XBINNING= 1 / Camera binning mode
YBINNING= 1 / Camera binning mode
XPIXSZ = 2.90000009536743 / [um] Pixel X axis size
YPIXSZ = 2.90000009536743 / [um] Pixel Y axis size
INSTRUME= 'Seestar S50' / Instrument name
CCD-TEMP= 14.625 / [degC] CCD temperature
GAIN = 80 / Sensor gain
BAYERPAT= 'GRBG ' / Bayer color pattern
FOCPOS = 1627 / [step] Focuser position
STACKCNT= 483 / Stack frames
OBJECT = 'Unknown ' / Name of the object of interest
SITELAT = 53.9811 / [deg] Observation site latitude
SITELONG= -1.32083 / [deg] Observation site longitude
RA = 324.250005 / [deg] Image center Right Ascension
DEC = 58.026389 / [deg] Image center Declination
CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions
CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions
CUNIT1 = 'deg ' / Unit of coordinates
CUNIT2 = 'deg ' / Unit of coordinates
EQUINOX = 9.87654321E+107 / Equatorial equinox
CRPIX1 = 749.01163737 / Axis1 reference pixel
CRPIX2 = 1971.998372396 / Axis2 reference pixel
CRVAL1 = 324.414574482 / [deg] Axis1 reference value
CRVAL2 = 57.5809898414 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000659380106962164 / [deg] X pixel size
CDELT2 = 0.000659999041023341 / [deg] Y pixel size
PC1_1 = 0.672936096450148 / Linear transformation matrix (1, 1)
PC1_2 = 0.739700621937306 / Linear transformation matrix (1, 2)
PC2_1 = 0.740197994068332 / Linear transformation matrix (2, 1)
PC2_2 = -0.672388971933075 / Linear transformation matrix (2, 2)
A_ORDER = 2 / SIP polynomial degree, axis 1, pixel-to-sky
A_0_0 = 0.
A_1_0 = 0.
A_0_1 = 0.
A_2_0 = 7.8653792092E-08
A_1_1 = 2.134952897935E-07
A_0_2 = 4.788079514115E-08
B_ORDER = 2 / SIP polynomial degree, axis 2, pixel-to-sky
B_0_0 = 0.
B_1_0 = 0.
B_0_1 = 0.
B_2_0 = 3.88120629391E-07
B_1_1 = 1.555713833405E-07
B_0_2 = -2.115963413525E-07
AP_ORDER= 2 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = -2.93118246966E-05
AP_1_0 = 7.39697841564E-08
AP_0_1 = 1.41520361647E-08
AP_2_0 = -7.8565650218E-08
AP_1_1 = -2.1341790896E-07
AP_0_2 = -4.787164820695E-08
BP_ORDER= 2 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = -6.48189083326E-07
BP_1_0 = 1.50144505009E-08
BP_0_1 = 2.38775300392E-07
BP_2_0 = -3.88002295791E-07
BP_1_1 = -1.55543354848E-07
BP_0_2 = 2.115716912465E-07
HISTORY Photometric CC (algorithm: PCC)
HISTORY SCNR (type=average neutral, amount=1.00, preserve=true)
HISTORY GraXpert BG extraction, smoothness 0.958
HISTORY GraXpert denoising, strength 0.800
HISTORY Saturation enhancement (amount=0.66)
HISTORY GHS pivot: 0.000, amount: 81.82, local: -3.57 [0.00 1.00]
HISTORY GHS LINEAR BP: 0.08
HISTORY GHS pivot: 0.000, amount: 12.92, local: -3.37 [0.00 1.00]
HISTORY GHS LINEAR BP: 0.02
HISTORY GHS pivot: 0.000, amount: 3.79, local: -3.37 [0.00 1.00]
HISTORY GHS LINEAR BP: 0.02
HISTORY Saturation enhancement (amount=0.79)
HISTORY NL-Bayes denoise (mod=1.000, CC enabled)
CREATOR = 'ZWO Seestar S50' / Capture software
PRODUCER= 'ZWO ' / Powered by ZWO
XORGSUBF= 0 / Subframe X position in binned pixels
YORGSUBF= 0 / Subframe Y position in binned pixels
EQMODE = 1 / Equatorial mode
CCDXBIN = 1 / Camera X Bin
CCDYBIN = 1 / Camera Y Bin
TOTALEXP= 9660. / Total Exposure Time in seconds
IMAGEW = 2160 / Image width, in pixels.
IMAGEH = 3840 / Image height, in pixels.
END
After dealing with integers, rational expressions, polynomials, etc all day, I have to come home and "demath" myself; Hence the more calm, relaxed look on my face.
Couldn't resist coding this polynomial in x/y.
Was in response to activity on Liberty BASIC- a programming language I play with. See www.diga.me.uk/in.html
Spring, 2009
Algebra II: graphing of polynomials, reducing them to prime factors, and then graphing them. This was my response.
How do you Determine if a Polynomial is the Difference of Two Squares By the term polynomial we Mean the different terms which are written one after another with the operation of addition or subtraction. We have different identities, which help us to solve and factorize the given polynomial. We just need to learn the method of identifying which type of polynomial is it and with which identity it is related to.
SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 6248 / length of data axis 1
NAXIS2 = 4176 / length of data axis 2
NAXIS3 = 3 / length of data axis 3
EXTEND = T / FITS dataset may contain extensions
COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy
COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H
BZERO = 0. / Offset data range to that of unsigned short
BSCALE = 1. / Default scaling factor
PROGRAM = 'Siril 1.4.0-beta2' / Software that created this HDU
DATE = '2025-06-20T16:01:43' / UTC date that FITS file was created
DATE-OBS= '2025-06-19T04:31:21.852702' / YYYY-MM-DDThh🇲🇲ss observation start,
IMAGETYP= 'Light ' / Type of image
ROWORDER= 'BOTTOM-UP' / Order of the rows in image array
EXPTIME = 180. / [s] Exposure time duration
TELESCOP= 'EQMod Mount' / Telescope used to acquire this image
FOCALLEN= 249. / [mm] Focal length
XBINNING= 1 / Camera binning mode
YBINNING= 1 / Camera binning mode
XPIXSZ = 3.75999999046326 / [um] Pixel X axis size
YPIXSZ = 3.75999999046326 / [um] Pixel Y axis size
INSTRUME= 'ZWO ASI2600MC Pro' / Instrument name
CCD-TEMP= 0. / [degC] CCD temperature
SET-TEMP= 0. / [degC] CCD temperature setpoint
GAIN = 100 / Sensor gain
OFFSET = 50 / Sensor gain offset
CVF = 0.242862924933434 / [e-/ADU] Electrons per A/D unit
STACKCNT= 108 / Stack frames
LIVETIME= 19440. / [s] Exposure time after deadtime correction
EXPSTART= 2460843.70360285 / [JD] Exposure start time (standard Julian date)
EXPEND = 2460846.68632973 / [JD] Exposure end time (standard Julian date)
OBJECT = 'IC4604 ' / Name of the object of interest
SITELAT = 34.1986 / [deg] Observation site latitude
SITELONG= -118.919 / [deg] Observation site longitude
OBJCTRA = '16 25 9.666' / [H M S] Image center Right Ascension
OBJCTDEC= '-24 58 16.731' / [D M S] Image center Declination
RA = 246.290273515059 / [deg] Image center Right Ascension
DEC = -24.9713141865654 / [deg] Image center Declination
CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions
CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions
CUNIT1 = 'deg ' / Unit of coordinates
CUNIT2 = 'deg ' / Unit of coordinates
EQUINOX = 9.87654321E+107 / Equatorial equinox
CRPIX1 = 2599.19637044 / Axis1 reference pixel
CRPIX2 = 2892.73217773 / Axis2 reference pixel
CRVAL1 = 245.620670819 / [deg] Axis1 reference value
CRVAL2 = -24.4042764421 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000864700998374305 / [deg] X pixel size
CDELT2 = 0.000865319529236372 / [deg] Y pixel size
PC1_1 = 0.172271849683372 / Linear transformation matrix (1, 1)
PC1_2 = 0.985049445361333 / Linear transformation matrix (1, 2)
PC2_1 = -0.984871415512921 / Linear transformation matrix (2, 1)
PC2_2 = 0.173286741863236 / Linear transformation matrix (2, 2)
A_ORDER = 2 / SIP polynomial degree, axis 1, pixel-to-sky
A_0_0 = 0.
A_1_0 = 0.
A_0_1 = 0.
A_2_0 = 2.48864416627E-07
A_1_1 = -3.91946256829E-07
A_0_2 = 4.53859301234E-08
B_ORDER = 2 / SIP polynomial degree, axis 2, pixel-to-sky
B_0_0 = 0.
B_1_0 = 0.
B_0_1 = 0.
B_2_0 = -2.96058644787E-08
B_1_1 = 2.34170076985E-07
B_0_2 = -4.24046924232E-07
AP_ORDER= 2 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = -0.00169119855281
AP_1_0 = 7.34918360459E-07
AP_0_1 = -9.76473604131E-07
AP_2_0 = -2.48340171849E-07
AP_1_1 = 3.90956395689E-07
AP_0_2 = -4.50595925707E-08
BP_ORDER= 2 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = 0.00130776632579
BP_1_0 = -3.35415770107E-07
BP_0_1 = 4.97999232371E-07
BP_2_0 = 2.94422197153E-08
BP_1_1 = -2.3337111896E-07
BP_0_2 = 4.2294922188E-07
HISTORY GraXpert AI BGE: subtraction
HISTORY Photometric CC (algorithm: PCC)
HISTORY SCNR (type=average neutral, amount=1.00, preserve=true)
HISTORY Histogram Transf. (mid=0.000, lo=0.002, hi=1.000)
CREATOR = 'ZWO ASIAIR Plus' / Capture software
XORGSUBF= 0 / Subframe X position in binned pixels
YORGSUBF= 0 / Subframe Y position in binned pixels
CCDXBIN = 1 / Camera X Bin
CCDYBIN = 1 / Camera Y Bin
GUIDECAM= 'ZWO ASI120MM Mini' / Guide camera model
IMAGEW = 6248 / Image width, in pixels.
IMAGEH = 4176 / Image height, in pixels.
END
SIMPLE = T / file does conform to FITS standard
BITPIX = 16 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 5305 / length of data axis 1
NAXIS2 = 3947 / length of data axis 2
NAXIS3 = 3 / length of data axis 3
EXTEND = T / FITS dataset may contain extensions
COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy
COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H
BZERO = 0. / Offset data range to that of unsigned short
BSCALE = 1. / Default scaling factor
PROGRAM = 'Siril 1.4.0-beta3' / Software that created this HDU
DATE = '2025-08-31T19:48:40' / UTC date that FITS file was created
DATE-OBS= '2025-08-30T06:44:05.682331' / YYYY-MM-DDThh🇲🇲ss observation start,
ROWORDER= 'TOP-DOWN' / Order of the rows in image array
EXPTIME = 1830. / [s] Exposure time duration
OBSERVER= 'DaveMartin' / Observer name
FILTER = 'mixed ' / Active filter name
FOCALLEN= 350.737 / [mm] Focal length
CENTALT = 54.9986111111111 / [deg] Altitude of telescope
CENTAZ = 317.111111111111 / [deg] Azimuth of telescope
XBINNING= 1 / Camera binning mode
YBINNING= 1 / Camera binning mode
XPIXSZ = 3.76 / [um] Pixel X axis size
YPIXSZ = 3.76 / [um] Pixel Y axis size
INSTRUME= 'ZWO ASI2600MC Pro' / Instrument name
CCD-TEMP= 0. / [degC] CCD temperature
SET-TEMP= 0. / [degC] CCD temperature setpoint
GAIN = 100 / Sensor gain
OFFSET = 12 / Sensor gain offset
CVF = 0.2636 / [e-/ADU] Electrons per A/D unit
FOCPOS = 33178 / [step] Focuser position
FOCTEMP = 11.8599996566772 / [degC] Focuser temperature
OBJECT = 'SH2-131 (Elephant' / Name of the object of interest
AIRMASS = 1.21983318371154 / Airmass at frame center (Gueymard 1993)
SITELAT = 39.3488888888889 / [deg] Observation site latitude
SITELONG= -78.8116666666667 / [deg] Observation site longitude
OBJCTRA = '21 39 20.786' / [H M S] Image center Right Ascension
OBJCTDEC= '+57 29 27.840' / [D M S] Image center Declination
RA = 324.836610257537 / [deg] Image center Right Ascension
DEC = 57.4910666057748 / [deg] Image center Declination
CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions
CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions
CUNIT1 = 'deg ' / Unit of coordinates
CUNIT2 = 'deg ' / Unit of coordinates
EQUINOX = 2000. / Equatorial equinox
CRPIX1 = 2672.5 / Axis1 reference pixel
CRPIX2 = 2050.5 / Axis2 reference pixel
CRVAL1 = 324.747824907617 / [deg] Axis1 reference value
CRVAL2 = 57.4824553633667 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000614246927725233 / [deg] X pixel size
CDELT2 = 0.000614206279736693 / [deg] Y pixel size
PC1_1 = 0.0703084306141619 / Linear transformation matrix (1, 1)
PC1_2 = 0.997525300222793 / Linear transformation matrix (1, 2)
PC2_1 = -0.997523181919709 / Linear transformation matrix (2, 1)
PC2_2 = 0.0703384783228858 / Linear transformation matrix (2, 2)
A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky
A_0_0 = 0.
A_1_0 = 0.
A_0_1 = 0.
A_2_0 = 4.89066047335137E-08
A_1_1 = -1.13699260318849E-07
A_0_2 = 8.88087755245384E-09
A_3_0 = -3.60518222915414E-11
A_2_1 = 1.99430347807434E-12
A_1_2 = -4.29462526384469E-11
A_0_3 = 5.24288869933521E-12
B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky
B_0_0 = 0.
B_1_0 = 0.
B_0_1 = 0.
B_2_0 = 4.30983502497688E-09
B_1_1 = 5.4146437330906E-08
B_0_2 = -8.88925649093415E-08
B_3_0 = 4.12794324800495E-12
B_2_1 = -3.74618908909417E-11
B_1_2 = -1.00543801866771E-12
B_0_3 = -3.94613448307762E-11
AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = 0.000139740010779307
AP_1_0 = -1.82239358159642E-07
AP_0_1 = -8.4138737291895E-08
AP_2_0 = -4.90148985454187E-08
AP_1_1 = 1.13913781653622E-07
AP_0_2 = -8.92446734610106E-09
AP_3_0 = 3.61155920306058E-11
AP_2_1 = -2.01516667479249E-12
AP_1_2 = 4.30465296034464E-11
AP_0_3 = -5.23184577751946E-12
BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = -0.000115849746318576
BP_1_0 = -2.59611120412717E-08
BP_0_1 = -1.14540555151699E-07
BP_2_0 = -4.28394848362944E-09
BP_1_1 = -5.42484460901311E-08
BP_0_2 = 8.90212701461562E-08
BP_3_0 = -4.1315140701688E-12
BP_2_1 = 3.75267800275289E-11
BP_1_2 = 9.97567010975472E-13
BP_0_3 = 3.95212136605438E-11
HISTORY Photometric CC (algorithm: SPCC)
PIERSIDE= 'EAST' /
CAMID = '1E1E560D0B020900' /
ADCBITS = 16 / Bit depth of camera sensor ADC in current mode
BIASADU = 121.16593933105469 / ADU for bias level (no photons) at current sett
EGAINSAV= 0.26355 / Electrons per ADU at saved bit depth
RELGAIN = 2.964 / Multiplicative gain relative to minumum
RDNOISE = 1.77 / Read noise in electrons
SUBEXP = 15 /
COLORTYP= 'RGB' /
DATE-END= '2025-08-30T07:27:08.7834822' / System Clock:Est. Frame End
DATE-AVG= '2025-08-30T07:05:37.2329070' / System Clock:Est. Frame Mid Point
JD_UTC = 2460917.7955698255 / Julian Date at mid exposure
END
Polynomial Diffusion Models for Life Insurance Liabilities. Biagini, Zhang arxiv.org/abs/1602.07910 #q-fin
Polynomial Diffusion Models for Life Insurance Liabilities. Biagini, Zhang arxiv.org/abs/1602.07910 #q-fin
His machines were considered the first computers in history. He made 2 different engines; the first engine was called the Difference Engine, and the Analytical Engine. The DIfference Engine could multiply or add but also could create tables of the results of up to seven-degree polynomial functions (cs.stanford.edu). Both of these engines were worked on between 1833-1871 ( howstuffworks.com).