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poly2bernstein : THEORY
BEGIN
IMPORTING multi_polynomial,
multi_bernstein
polydegmono,
bsdegmono : VAR DegreeMono
pprod : VAR Polyproduct
mpoly : VAR MultiPolynomial
nvars,terms : VAR posnat
cf : VAR Coeff
bs_convert_mono(pprod,polydegmono,bsdegmono,nvars)(j:nat)(s:nat): real =
IF s>bsdegmono(j) THEN 0
ELSE sigma(0,s,LAMBDA(i:nat):IF i>s OR i>polydegmono(j) THEN 0
ELSE pprod(j)(i)*(C(s,i)/C(bsdegmono(j),i))
ENDIF)
ENDIF
bs_convert_poly(mpoly,polydegmono,bsdegmono,nvars,terms)(r:nat): Polyproduct =
bs_convert_mono(mpoly(r),polydegmono,bsdegmono,nvars)
bs_convert_poly_def: LEMMA le_below_mono?(nvars)(polydegmono,bsdegmono) IMPLIES
multipoly_eval(mpoly,polydegmono,cf,nvars,terms) =
multibs_eval(bs_convert_poly(mpoly,polydegmono,bsdegmono,nvars,terms),
bsdegmono,cf,nvars,terms)
END poly2bernstein
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