- Timestamp:
- 2015-06-05T11:18:00-07:00 (10 years ago)
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-
- 1 edited
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branches/f4grobner/polynomial.lisp
r53 r55 188 188 (coerce-coeff ring expr vars))))))) 189 189 190 191 190 (defun spoly (ring f g) 191 "It yields the S-polynomial of polynomials F and G." 192 (declare (type poly f g)) 193 (let* ((lcm (monom-lcm (poly-lm f) (poly-lm g))) 194 (mf (monom-div lcm (poly-lm f))) 195 (mg (monom-div lcm (poly-lm g)))) 196 (declare (type monom mf mg)) 197 (multiple-value-bind (c cf cg) 198 (funcall (ring-ezgcd ring) (poly-lc f) (poly-lc g)) 199 (declare (ignore c)) 200 (poly-sub 201 ring 202 (scalar-times-poly ring cg (monom-times-poly mf f)) 203 (scalar-times-poly ring cf (monom-times-poly mg g)))))) 204 205 206 (defun poly-primitive-part (ring p) 207 "Divide polynomial P with integer coefficients by gcd of its 208 coefficients and return the result." 209 (declare (type poly p)) 210 (if (poly-zerop p) 211 (values p 1) 212 (let ((c (poly-content ring p))) 213 (values (make-poly-from-termlist (mapcar 214 #'(lambda (x) 215 (make-term (term-monom x) 216 (funcall (ring-div ring) (term-coeff x) c))) 217 (poly-termlist p)) 218 (poly-sugar p)) 219 c)))) 220 221 (defun poly-content (ring p) 222 "Greatest common divisor of the coefficients of the polynomial P. Use the RING structure 223 to compute the greatest common divisor." 224 (declare (type poly p)) 225 (reduce (ring-gcd ring) (mapcar #'term-coeff (rest (poly-termlist p))) :initial-value (poly-lc p)))
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