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what data structure for polinomial


 
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Old 10-07-2002
Question what data structure for polynomial

Hello, guys

Anyone had experiences to express polynomial using c language. I want to output the polynomial formula after I solve the question. Not to count the value of a polynomial.

That means I have to output the polynomial formula to screen.

such as:
f := p^100-4275+56*p^57+123*(1-p)^34 ;

362880*p^45-14515200*p^44+282592800*p^43-3567715200*p^42+32833495800*p^41-234748765440*p^40+1357020856800*p^39-6517548349200*p^38+26521978127400*p^37-92792729053500*p^36+282287441908080*p^35-753273866698920*p^34+1775448575926410*p^33-3716558335019880*p^32+6939551178972720*p^31-11596879696617600*p^30+17388982649046960*p^29-23437879996999860*p^28+28429756177413360*p^27-31050312703343640*p^26+30532209914200806*p^25-27011077082801580*p^24+21469710851551800*p^23-15300758477189520*p^22+9748958193896580*p^21-5532426738592740*p^20+2782630494934920*p^19-1232671556293800*p^18+477077447178540*p^17-159642667620135*p^16+45558310696800*p^15-10884316965480*p^14+2121183237600*p^13-324496267200*p^12+36628300800*p^11-2719892160*p^10+100000000*p^9;

This can be done beatifully by Maple.But I do not know how they do this.


Last edited by xli3; 11-01-2002 at 09:48 PM..
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mlib_ImagePolynomialWarp_Fp(3MLIB)			    mediaLib Library Functions				mlib_ImagePolynomialWarp_Fp(3MLIB)

NAME
mlib_ImagePolynomialWarp_Fp - polynomial-based image warp SYNOPSIS
cc [ flag... ] file... -lmlib [ library... ] #include <mlib.h> mlib_status mlib_ImagePolynomialWarp_Fp(mlib_image *dst, const mlib_image *src, const mlib_d64 *xCoeffs, const mlib_d64 *yCoeffs, mlib_s32 n, mlib_d64 preShiftX, mlib_d64 preShiftY, mlib_d64 postShiftX, mlib_d64 postShiftY, mlib_d64 preScaleX, mlib_d64 preScaleY, mlib_d64 postScaleX, mlib_d64 postScaleY, mlib_filter filter, mlib_edge edge); DESCRIPTION
The mlib_ImagePolynomialWarp_Fp() function performs a polynomial-based image warp on a floating-point image. The images must have the same type, and the same number of channels. The images can have 1, 2, 3, or 4 channels. The data type of the images can be MLIB_FLOAT or MLIB_DOUBLE. The source and destination images may have different sizes. The xCoeffs and yCoeffs parameters must contain the same number of coefficients of the form (n + 1)(n + 2)/2 for some n, where n is the degree power of the polynomial. The coefficients, in order, are associated with the terms: 1, x, y, x**2, x*y, y**2, ..., x**n, x**(n-1)*y, ..., x*y**(n-1), y**n and coefficients of value 0 cannot be omitted. The image pixels are assumed to be centered at .5 coordinate points. In other words, the upper-left corner pixel of an image is located at (0.5, 0.5). For each pixel in the destination image, its center point D is backward mapped to a point S in the source image. Then the source pixels with their centers surrounding point S are selected to do one of the interpolations specified by the filter parameter to generate the pixel value for point D. The mapping is defined by the two bivariate polynomial functions X(x, y) and Y(x, y) that map destination (x, y) coordinates to source X and Y positions respectively. The functions X(x, y) and Y(x, y) are: preX = (x + preShiftX)*preScaleX preY = (y + preShiftY)*preScaleY n i warpedX = SUM {SUM {xCoeffs_ij * preX**(i-j) * preY**j}} i=0 j=0 n i warpedY = SUM {SUM {yCoeffs_ij * preX**(i-j) * preY**j}} i=0 j=0 X(x, y) = warpedX*postScaleX - postShiftX Y(x, y) = warpedY*postScaleY - postShiftY The destination (x, y) coordinates are pre-shifted by (preShiftX, preShiftY) and pre-scaled by the factors preScaleX and preScaleY prior to the evaluation of the polynomial. The results of the polynomial evaluations are scaled by postScaleX and postScaleY, and then shifted by (-postShiftX, -postShiftY) to produce the source pixel coordinates. This process allows for better precision of the results and supports tiled images. PARAMETERS
The function takes the following arguments: dst Pointer to destination image. src Pointer to source image. xCoeffs Destination to source transform coefficients for the X coordinate. yCoeffs Destination to source transform coefficients for the Y coordinate. n Degree power of the polynomial. preShiftX Displacement to apply to destination X positions. preShiftY Displacement to apply to destination Y positions. postShiftX Displacement to apply to source X positions. postShiftY Displacement to apply to source Y positions. preScaleX Scale factor to apply to destination X positions. preScaleY Scale factor to apply to destination Y positions. postScaleX Scale factor to apply to source X positions. postScaleY Scale factor to apply to source Y positions. filter Type of resampling filter. It can be one of the following: MLIB_NEAREST MLIB_BILINEAR MLIB_BICUBIC MLIB_BICUBIC2 edge Type of edge condition. It can be one of the following: MLIB_EDGE_DST_NO_WRITE MLIB_EDGE_SRC_PADDED RETURN VALUES
The function returns MLIB_SUCCESS if successful. Otherwise it returns MLIB_FAILURE. ATTRIBUTES
See attributes(5) for descriptions of the following attributes: +-----------------------------+-----------------------------+ | ATTRIBUTE TYPE | ATTRIBUTE VALUE | +-----------------------------+-----------------------------+ |Interface Stability |Evolving | +-----------------------------+-----------------------------+ |MT-Level |MT-Safe | +-----------------------------+-----------------------------+ SEE ALSO
mlib_ImagePolynomialWarp(3MLIB), mlib_ImagePolynomialWarpTable(3MLIB), mlib_ImagePolynomialWarpTable_Fp(3MLIB), attributes(5) SunOS 5.10 10 Nov 2004 mlib_ImagePolynomialWarp_Fp(3MLIB)

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