## what data structure for polinomial

what data structure for polinomial
# 1
10-07-2002
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..
 xli3 View Public Profile for xli3 Find all posts by xli3

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```mlib_ImagePolynomialWarp(3MLIB) 			    mediaLib Library Functions				   mlib_ImagePolynomialWarp(3MLIB)

NAME
mlib_ImagePolynomialWarp - polynomial-based image warp

SYNOPSIS
cc [ flag... ] file... -lmlib [ library... ]
#include <mlib.h>

mlib_status mlib_ImagePolynomialWarp(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() function performs a polynomial-based image warp.

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_BYTE, MLIB_SHORT, MLIB_USHORT, or MLIB_INT. 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

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	     |Committed 		   |
+-----------------------------+-----------------------------+
|MT-Level		     |MT-Safe			   |
+-----------------------------+-----------------------------+