diff options
Diffstat (limited to 'src/algebra/gpgcd.spad.pamphlet')
| -rw-r--r-- | src/algebra/gpgcd.spad.pamphlet | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/src/algebra/gpgcd.spad.pamphlet b/src/algebra/gpgcd.spad.pamphlet index bf758915..85f20722 100644 --- a/src/algebra/gpgcd.spad.pamphlet +++ b/src/algebra/gpgcd.spad.pamphlet @@ -139,7 +139,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where => g*gcd(c1,c2)::SUPP -- divdes them both, so is the gcd v:=variables g -- there can be at most these variables in answer v1:=setDifference(vp1,v) - if #v1 ^= 0 then + if #v1 ~= 0 then g:=recursivelyGCDCoefficients(g,v,p1,v1) -- one? g => return gcd(c1,c2)::SUPP (g = 1) => return gcd(c1,c2)::SUPP @@ -222,7 +222,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where g:=monomial(lcp,degree gR)+map(#1::P,reductum gR) cf:=monomial(lcp,degree cfR)+map(#1::P,reductum cfR) p:=lcp*p -- impose leaidng coefficient of p on each factor - while lv ^= [] repeat + while lv ~= [] repeat v:=first lv r:=first lr lv:=rest lv @@ -243,7 +243,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where g:=g+pn*first step cf:=cf+pn*second step pn:=pn*prime - thisp ^= g*cf => return "failed" + thisp ~= g*cf => return "failed" g recursivelyGCDCoefficients(g:SUPP,v:List OV,p:SUPP,pv:List OV) == mv:=first pv -- take each coefficient w.r.t. mv @@ -256,7 +256,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where else g:=recursivelyGCDCoefficients(p,v,p1,pv) -- one? g => return 1 (g = 1) => return 1 - g^=oldg => + g~=oldg => oldv:=v v:=variables g pv:=setUnion(pv,setDifference(v,oldv)) @@ -265,7 +265,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where #lv = 0 => p1 lr:=[ randomR() for vv in lv] dg:=degree p1 - while dg ^= degree (ans:= map(eval(#1,lv,lr),p1)) repeat + while dg ~= degree (ans:= map(eval(#1,lv,lr),p1)) repeat lr:=[ randomR() for vv in lv] ans -- eval(p1:SUPP,lv:List OV,lr:List R) == map(eval(#1,lv,lr),p1) @@ -305,9 +305,9 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD range:=2*range --JHD lval:=[(random()$I rem (2*range) - range)::R for i in 1..nvr] --JHD uf1:SUPR:=univariate eval(p1,lvr,lval) ---JHD degree uf1 ^= d1 => "new point" +--JHD degree uf1 ~= d1 => "new point" --JHD uf2:SUPR:=univariate eval(p2,lvr,lval) ---JHD degree uf2 ^= d2 => "new point" +--JHD degree uf2 ~= d2 => "new point" --JHD u:=gcd(uf1,uf2) --JHD du:=degree u --JHD --the univariate gcd is 1 @@ -324,7 +324,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD dd=d1 => --JHD if ^((f:=p2 exquo p1) case "failed") then --JHD return [[u],lval,p1]$UTerm ---JHD if dd^=d2 then dd:=(dd-1)::NNI +--JHD if dd~=d2 then dd:=(dd-1)::NNI --JHD --JHD dd=d2 => --JHD if ^((f:=p1 exquo p2) case "failed") then @@ -369,7 +369,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD (gd1,gd2):=(l,l) --JHD ul:=univariate(eval(l,lvar1,lval)) --JHD dl:=degree ul ---JHD if degree gcd(ul,differentiate ul) ^=0 then +--JHD if degree gcd(ul,differentiate ul) ~=0 then --JHD newchoice:=good(l,lvar.rest) --JHD ul:=newchoice.upol --JHD lval:=newchoice.inval @@ -381,7 +381,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD d:SUPR:=gcd(cons(ul,ulist)) --JHD if degree d =0 then return gd1 --JHD lquo:=(ul exquo d)::SUPR ---JHD if degree lquo ^=0 then +--JHD if degree lquo ~=0 then --JHD lgcd:=gcd(cons(leadingCoefficient univariate(l,x),lcpol)) --JHD gd2:=lift(l,d,lquo,lgcd,lvar,ldeg,lval) --JHD l:=gd2 @@ -546,7 +546,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD df:=degree(f,x) --JHD leadlist:List(P):=[] --JHD ---JHD if lgcd^=1$P then +--JHD if lgcd~=1$P then --JHD leadpol:=true --JHD f:=lgcd*f --JHD ldeg:=[n0+n1 for n0 in ldeg for n1 in degree(lgcd,lvar)] @@ -558,7 +558,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD lg:=imposelc([d,uf],lvar,lval,leadlist) --JHD plist:=lifting(univariate(f,x),lvar,lg,lval,leadlist,ldeg)::List P --JHD (p0:P,p1:P):=(plist.first,plist.2) ---JHD if univariate eval(p0,rest lvar,lval) ^= lg.first then +--JHD if univariate eval(p0,rest lvar,lval) ~= lg.first then --JHD (p0,p1):=(p1,p0) --JHD ^leadpol => p0 --JHD cprim:=contprim([p0]) |