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fixed a symbol conflict involving resultants and discriminants
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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@@ -14,6 +14,7 @@ newPackage( | |
| Authors => {{Name => "Giovanni Staglianò", Email => "[email protected]"}}, | ||
| Headline => "resultants, discriminants, and Chow forms", | ||
| Keywords => {"Commutative Algebra"}, | ||
| PackageExports => { "Elimination" }, | ||
| Certification => { | ||
| "journal name" => "The Journal of Software for Algebra and Geometry", | ||
| "journal URI" => "http://j-sag.org/", | ||
|
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@@ -31,8 +32,9 @@ newPackage( | |
| ) | ||
|
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| export{ | ||
| "resultant", | ||
| "discriminant", | ||
| -- these two come from Elimination | ||
| --"resultant", | ||
| --"discriminant", | ||
| "affineResultant", | ||
| "affineDiscriminant", | ||
| "genericPolynomials", | ||
|
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@@ -61,25 +63,24 @@ export{ | |
| ---------------------------------------------------------------------------------- | ||
| ----------------------- MultipolynomialResultats --------------------------------- | ||
| ---------------------------------------------------------------------------------- | ||
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| resultant = method(TypicalValue => RingElement, Options => {Algorithm => "Poisson"}); | ||
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| resultant (Matrix) := o -> (F) -> ( | ||
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| resultant Matrix := RingElement => opts -> F -> ( | ||
| if numgens target F != 1 then error "expected a matrix with one row"; | ||
| if not isPolynomialRing ring F then error "the base ring must be a polynomial ring"; | ||
| n := numgens source F -1; | ||
| if n+1 != numgens ring F then error("the number of polynomials must be equal to the number of variables, but got " | toString(numgens source F) | " polynomials and " | toString(numgens ring F) | " variables"); | ||
| if o.Algorithm =!= "Poisson" and o.Algorithm =!= "Poisson2" and o.Algorithm =!= "Macaulay" and o.Algorithm =!= "Macaulay2" then error "bad value for option Algorithm; possible values are \"Poisson\", \"Poisson2\", \"Macaulay\", and \"Macaulay2\""; | ||
| algorithm := if opts.Algorithm === null then "Poisson" else opts.Algorithm; | ||
| if not member(algorithm, {"Poisson", "Poisson2", "Macaulay", "Macaulay2"}) then error "bad value for option Algorithm; possible values are \"Poisson\", \"Poisson2\", \"Macaulay\", and \"Macaulay2\""; | ||
| K := coefficientRing ring F; | ||
| x := local x; | ||
| Pn := K[x_0..x_n]; | ||
| F = sub(F,vars Pn); F' := F; | ||
| d := apply(flatten entries F,ee->first degree ee); | ||
| if not isField K then (K' := frac K; Pn' := K'[x_0..x_n]; F' = sub(F,Pn')); | ||
| if not isHomogeneous ideal F' then error("expected homogeneous polynomials"); | ||
| if o.Algorithm === "Macaulay" then (if (min d > -1 and sum(d) > n) then return MacaulayResultant(F,false) else <<"--warning: ignored option Algorithm=>\"Macaulay\""<<endl); | ||
| if o.Algorithm === "Poisson2" then return interpolateRes(F,"Poisson"); | ||
| if o.Algorithm === "Macaulay2" then return interpolateRes(F,"Macaulay"); | ||
| if algorithm === "Macaulay" then (if (min d > -1 and sum(d) > n) then return MacaulayResultant(F,false) else <<"--warning: ignored option Algorithm=>\"Macaulay\""<<endl); | ||
| if algorithm === "Poisson2" then return interpolateRes(F,"Poisson"); | ||
| if algorithm === "Macaulay2" then return interpolateRes(F,"Macaulay"); | ||
| R := PoissonFormula F'; | ||
| if R != 0 then ( | ||
| if isField K then return R; | ||
|
|
@@ -88,7 +89,7 @@ resultant (Matrix) := o -> (F) -> ( | |
| if dim ideal F' > 0 then sub(0,K) else resultant(wobble F,Algorithm=>"Poisson") | ||
| ); | ||
|
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||
| resultant (List) := o -> (s) -> resultant(matrix{s},Algorithm=>o.Algorithm); | ||
| resultant List := RingElement => opts -> s -> resultant(matrix {s}, opts); | ||
|
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||
| PoissonFormula = method(); | ||
| PoissonFormula (Matrix) := (F) -> ( | ||
|
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@@ -228,15 +229,13 @@ Res222 = (F) -> ( | |
| sub(W,apply(20,j -> g_j => mm_j)) | ||
| ); | ||
|
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| discriminant = method(TypicalValue => RingElement, Options => {Algorithm => "Poisson"}); | ||
|
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| discriminant RingElement := o -> (G) -> ( | ||
| discriminant RingElement := RingElement => opts -> G -> ( | ||
| if not (isPolynomialRing ring G) then error "expected a homogeneous polynomial"; | ||
| -- if not (isHomogeneous G) then error "expected a homogeneous polynomial"; | ||
| n := numgens ring G; | ||
| d := first degree G; | ||
| a := lift(((d-1)^n - (-1)^n)/d,ZZ); | ||
| resG := resultant(transpose jacobian matrix{{G}},Algorithm=>o.Algorithm); | ||
| resG := resultant(transpose jacobian matrix{{G}}, opts); | ||
| try return lift(resG/(d^a),ring resG) else (try (q := first quotientRemainder(resG,d^a); assert(resG == q*d^a); return q) else (<<"--warning: the returned discriminant value is only correct up to a non-zero multiplicative constant"<<endl; return resG;)); | ||
| ); | ||
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@@ -849,7 +848,7 @@ beginDocumentation() | |
| document { | ||
| Key => Resultants, | ||
| Headline => "resultants, discriminants, and Chow forms", | ||
| PARA{"This package provides methods to deal with resultants and discriminants of multivariate polynomials, and with higher associated subvarieties of irreducible projective varieties. The main methods are: ", TO "resultant",", ",TO "discriminant",", ", TO "chowForm",", ",TO "dualVariety",", and ",TO "tangentialChowForm",". For the mathematical theory, we refer to the following two books: ", HREF{"http://link.springer.com/book/10.1007%2Fb138611","Using Algebraic Geometry"},", by David A. Cox, John Little, Donal O'shea; ", HREF{"http://link.springer.com/book/10.1007%2F978-0-8176-4771-1","Discriminants, Resultants, and Multidimensional Determinants"},", by Israel M. Gelfand, Mikhail M. Kapranov and Andrei V. Zelevinsky. Other references for the theory of Chow forms are: ", HREF{"https://projecteuclid.org/euclid.dmj/1077305197","The equations defining Chow varieties"}, ", by M. L. Green and I. Morrison; ", HREF{"http://link.springer.com/article/10.1007/BF02567693","Multiplicative properties of projectively dual varieties"},", by J. Weyman and A. Zelevinsky; and ",HREF{"https://www.sciencedirect.com/science/article/abs/pii/S0747717119301506","Coisotropic hypersurfaces in Grassmannians"}, ", by K. Kohn."}, | ||
| PARA{"This package provides methods to deal with resultants and discriminants of multivariate polynomials, and with higher associated subvarieties of irreducible projective varieties. The main methods are: ", TO (resultant,Matrix),", ",TO (discriminant,RingElement),", ", TO "chowForm",", ",TO "dualVariety",", and ",TO "tangentialChowForm",". For the mathematical theory, we refer to the following two books: ", HREF{"http://link.springer.com/book/10.1007%2Fb138611","Using Algebraic Geometry"},", by David A. Cox, John Little, Donal O'shea; ", HREF{"http://link.springer.com/book/10.1007%2F978-0-8176-4771-1","Discriminants, Resultants, and Multidimensional Determinants"},", by Israel M. Gelfand, Mikhail M. Kapranov and Andrei V. Zelevinsky. Other references for the theory of Chow forms are: ", HREF{"https://projecteuclid.org/euclid.dmj/1077305197","The equations defining Chow varieties"}, ", by M. L. Green and I. Morrison; ", HREF{"http://link.springer.com/article/10.1007/BF02567693","Multiplicative properties of projectively dual varieties"},", by J. Weyman and A. Zelevinsky; and ",HREF{"https://www.sciencedirect.com/science/article/abs/pii/S0747717119301506","Coisotropic hypersurfaces in Grassmannians"}, ", by K. Kohn."}, | ||
| } | ||
| document { | ||
| Key => {[resultant,Algorithm],[discriminant,Algorithm],[affineResultant,Algorithm],[affineDiscriminant,Algorithm]}, | ||
|
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@@ -868,10 +867,10 @@ document { | |
| "time resultant(F,Algorithm=>\"Macaulay\")", | ||
| "assert(o3 == o4 and o4 == o5 and o5 == o6)" | ||
| }, | ||
| SeeAlso => {discriminant,resultant} | ||
| SeeAlso => {(discriminant,RingElement),(resultant,Matrix)} | ||
| } | ||
| document { | ||
| Key => {resultant,(resultant,Matrix),(resultant,List)}, | ||
| Key => {(resultant,Matrix),(resultant,List)}, | ||
| Headline => "multipolynomial resultant", | ||
| Usage => "resultant F", | ||
| Inputs => { "F" => Matrix => {"a row matrix whose entries are ", TEX///$n+1$///," homogeneous polynomials ", TEX///$F_0,\ldots,F_n$///," in ", TEX///$n+1$///," variables (or a ", TO2{List,"list"}," to be interpreted as such a matrix)"}}, | ||
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@@ -892,15 +891,18 @@ document { | |
| "F = genericPolynomials({2,2,2},ZZ)", | ||
| "time # terms resultant F" | ||
| }, | ||
| SeeAlso => {chowForm,discriminant} | ||
| SeeAlso => {chowForm,(discriminant,RingElement)} | ||
| } | ||
| document { | ||
| Key => {discriminant,(discriminant,RingElement)}, | ||
| Key => {(discriminant,RingElement)}, | ||
| Headline => "resultant of the partial derivatives", | ||
| Usage => "discriminant F", | ||
| Inputs => { "F" => RingElement => {"a homogeneous polynomial"}}, | ||
| Outputs => {RingElement => {"the discriminant of ",TT "F"}}, | ||
| PARA{"The discriminant of a homogeneous polynomial is defined, up to a scalar factor, as the ",TO resultant," of its partial derivatives. For the general theory, see one of the following: ",HREF{"http://link.springer.com/book/10.1007%2Fb138611","Using Algebraic Geometry"},", by David A. Cox, John Little, Donal O'shea; ", HREF{"http://link.springer.com/book/10.1007%2F978-0-8176-4771-1","Discriminants, Resultants, and Multidimensional Determinants"},", by Israel M. Gelfand, Mikhail M. Kapranov and Andrei V. Zelevinsky."}, | ||
| PARA{"The discriminant of a homogeneous polynomial is defined, up to a scalar factor, as the ", | ||
| TO (resultant,Matrix)," of its partial derivatives. For the general theory, see one of the following: ", | ||
| HREF{"http://link.springer.com/book/10.1007%2Fb138611","Using Algebraic Geometry"},", by David A. Cox, John Little, Donal O'shea; ", | ||
| HREF{"http://link.springer.com/book/10.1007%2F978-0-8176-4771-1","Discriminants, Resultants, and Multidimensional Determinants"},", by Israel M. Gelfand, Mikhail M. Kapranov and Andrei V. Zelevinsky."}, | ||
| EXAMPLE { | ||
| "ZZ[a,b,c][x,y]; F = a*x^2+b*x*y+c*y^2", | ||
| "time discriminant F", | ||
|
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@@ -917,7 +919,7 @@ document { | |
| "time D=discriminant pencil", | ||
| "factor D" | ||
| }, | ||
| SeeAlso => {dualVariety,resultant} | ||
| SeeAlso => {dualVariety,(resultant,Matrix)} | ||
| } | ||
| document { | ||
| Key => {affineResultant,(affineResultant,Matrix),(affineResultant,List)}, | ||
|
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@@ -930,7 +932,7 @@ document { | |
| "f = {3*t*y*z-u*z^2+1, -y+t+3*u-1, u*z^4-t*y^3+t*y*z}", | ||
| "affineResultant f" | ||
| }, | ||
| SeeAlso => {resultant,affineDiscriminant} | ||
| SeeAlso => {(resultant,Matrix),affineDiscriminant} | ||
| } | ||
| document { | ||
| Key => {affineDiscriminant,(affineDiscriminant,RingElement)}, | ||
|
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@@ -944,7 +946,7 @@ document { | |
| "ZZ[a,b,c,d][x]; f = a*x^3+b*x^2+c*x+d", | ||
| "affineDiscriminant f", | ||
| }, | ||
| SeeAlso => {discriminant,affineResultant} | ||
| SeeAlso => {(discriminant,RingElement),affineResultant} | ||
| } | ||
| document { | ||
| Key => {genericPolynomials,(genericPolynomials,VisibleList,Ring),(genericPolynomials,List)}, | ||
|
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@@ -976,7 +978,7 @@ document { | |
| "time (D,D') = macaulayFormula F", | ||
| "assert(det D == (resultant F) * (det D'))" | ||
| }, | ||
| SeeAlso => {resultant} | ||
| SeeAlso => {(resultant,Matrix)} | ||
| } | ||
| document { | ||
| Key => {veronese,(veronese,ZZ,ZZ,Ring),(veronese,ZZ,ZZ)}, | ||
|
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@@ -1238,7 +1240,7 @@ document { | |
| "time Z = dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true);", | ||
| "discF == sub(Z,vars ring discF) and Z == sub(discF,vars ring Z)" | ||
| }, | ||
| SeeAlso => {conormalVariety,discriminant} | ||
| SeeAlso => {conormalVariety,(discriminant,RingElement)} | ||
| } | ||
| document { | ||
| Key => {[conormalVariety,Strategy],[dualVariety,Strategy]}, | ||
|
|
||
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