Suppose we have a liste of polynomials L; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)): isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)): isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)): isolve(g3[1]);
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About Grobner basis
About Grobner basis
Suppose we have a liste of polynomials L; L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)): isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)): isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)): isolve(g3[1]);
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g2:=Basis(L,plex(z,w,x,y)): isolve(g2[1]);
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)):
isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)):
isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)):
isolve(g3[1]);
For exaple suppose, L=[xyz - 246887379411/1185925973883351194867115857111747299632057867623yzw, x^2 - 60953378112431066706921/1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129w^2, xw - 246887379411/1185925973883351194867115857111747299632057867623w^2]
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)):
isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)):
isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)):
isolve(g3[1]);
For exaple example suppose, L=[xyz - 246887379411/1185925973883351194867115857111747299632057867623yzw, x^2 - 60953378112431066706921/1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129w^2, xw - 246887379411/1185925973883351194867115857111747299632057867623w^2]
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)):
isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)):
isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)):
isolve(g3[1]);
For example suppose, L=[xL=[1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2 - 585580311734997207006635656684084836378829142925094427420106xw + 60953378112431066706921w^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2 + 242035925986271489335186642003579544694017559808139175285991673034916861xw + 22772877973564833308423102217214551w^2, 1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2y - 585580311734997207006635656684084836378829142925094427420106xyw + 60953378112431066706921yw^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2y + 242035925986271489335186642003579544694017559808139175285991673034916861xyz - 246887379411/1185925973883351194867115857111747299632057867623w + 22772877973564833308423102217214551yw^2, 546492971093875818200311226757760151716020675484639718374766505281329940973795540404028891234781638071786218379709560581xyz - 113769510467918507941520256906804857756761200776076799074471649913620059848042913417yzw, x^2 - 60953378112431066706921/1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129w^2, xw - 246887379411/1185925973883351194867115857111747299632057867623w^2]w]
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)):
isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)):
isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)):
isolve(g3[1]);
i.e. How to compute the grobner basis for the ideal generated by the list of polynomials L with respect to the order x<y<z<w and="" then="" with="" respect="" to="" the="" order="" z<w<x<y="" and="" finally="" with="" respect="" to="" the="" order="" w<y<z<x="" .<="" p="">
For example suppose, L=[1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2 - 585580311734997207006635656684084836378829142925094427420106xw + 60953378112431066706921w^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2 + 242035925986271489335186642003579544694017559808139175285991673034916861xw + 22772877973564833308423102217214551w^2, 1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2y - 585580311734997207006635656684084836378829142925094427420106xyw + 60953378112431066706921yw^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2y + 242035925986271489335186642003579544694017559808139175285991673034916861xyw + 22772877973564833308423102217214551yw^2, 546492971093875818200311226757760151716020675484639718374766505281329940973795540404028891234781638071786218379709560581xyz - 113769510467918507941520256906804857756761200776076799074471649913620059848042913417yzw]
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)):
isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)):
isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)):
isolve(g3[1]);
i.e. How to compute the grobner basis for the ideal generated by the list of polynomials L with respect to the order x<y<z<w and="" then="" with="" respect="" to="" the="" order="" z<w<x<y="" and="" finally="" with="" respect="" to="" the="" order="" w<y<z<x="" .<="" p="">
x < y < z < w and then with respect to the order z < w < x < y and finally with respect to the order w < y < z < x .
For example suppose, L=[1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2 - 585580311734997207006635656684084836378829142925094427420106xw + 60953378112431066706921w^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2 + 242035925986271489335186642003579544694017559808139175285991673034916861xw + 22772877973564833308423102217214551w^2, 1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2y - 585580311734997207006635656684084836378829142925094427420106xyw + 60953378112431066706921yw^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2y + 242035925986271489335186642003579544694017559808139175285991673034916861xyw + 22772877973564833308423102217214551yw^2, 546492971093875818200311226757760151716020675484639718374766505281329940973795540404028891234781638071786218379709560581xyz - 113769510467918507941520256906804857756761200776076799074471649913620059848042913417yzw]
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)):
isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)):
isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)):
isolve(g3[1]);
i.e. How to compute the grobner basis for the ideal generated by the list of polynomials L with respect to the order x < y < z < >y > z > w and then with respect to the order z < w < > w > x < > y and finally with respect to the order w < y < z < > y > z > x .
For example suppose, L=[1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2 - 585580311734997207006635656684084836378829142925094427420106xw + 60953378112431066706921w^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2 + 242035925986271489335186642003579544694017559808139175285991673034916861xw + 22772877973564833308423102217214551w^2, 1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2y - 585580311734997207006635656684084836378829142925094427420106xyw + 60953378112431066706921yw^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2y + 242035925986271489335186642003579544694017559808139175285991673034916861xyw + 22772877973564833308423102217214551yw^2, 546492971093875818200311226757760151716020675484639718374766505281329940973795540404028891234781638071786218379709560581xyz - 113769510467918507941520256906804857756761200776076799074471649913620059848042913417yzw]
About Grobner basis
Suppose we have a liste of polynomials L in Z[x,y,z,w] ; I need to transform the following code in Maple to Sage
g1:=Basis(L,plex(x,y,z,w)):
isolve(g1[1]);
g2:=Basis(L,plex(z,w,x,y)):
isolve(g2[1]);
g3:=Basis(L,plex(w,y,z,x)):
isolve(g3[1]);
i.e. How to compute the grobner basis for the ideal generated by the list of polynomials L with respect to the order x >y > z > w and then with respect to the order z > w > x > y and finally with respect to the order w > y > z > x .
For example suppose, L=[1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2
L=[1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129*x^2 - 585580311734997207006635656684084836378829142925094427420106xw 585580311734997207006635656684084836378829142925094427420106*x*w + 60953378112431066706921w^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2 60953378112431066706921*w^2,
-1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472*x^2 + 242035925986271489335186642003579544694017559808139175285991673034916861xw 242035925986271489335186642003579544694017559808139175285991673034916861*x*w + 22772877973564833308423102217214551w^2, 1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129x^2y 22772877973564833308423102217214551*w^2,
1406420415531174980327303290571117064276422184073371260430004727814077316258636748578133791670129*x^2*y - 585580311734997207006635656684084836378829142925094427420106xyw 585580311734997207006635656684084836378829142925094427420106*x*y*w + 60953378112431066706921yw^2, -1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472x^2y 60953378112431066706921*y*w^2,
-1688076693759028688508053956627434893445056753313490532106912447426325421979583194817700061681593440864404472*x^2*y + 242035925986271489335186642003579544694017559808139175285991673034916861xyw 242035925986271489335186642003579544694017559808139175285991673034916861*x*y*w + 22772877973564833308423102217214551yw^2, 546492971093875818200311226757760151716020675484639718374766505281329940973795540404028891234781638071786218379709560581xyz 22772877973564833308423102217214551*y*w^2,
546492971093875818200311226757760151716020675484639718374766505281329940973795540404028891234781638071786218379709560581*x*y*z - 113769510467918507941520256906804857756761200776076799074471649913620059848042913417yzw]113769510467918507941520256906804857756761200776076799074471649913620059848042913417*y*z*w]
