# Changeset f7d745 in git

Ignore:
Timestamp:
May 26, 2011, 1:55:32 PM (13 years ago)
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '021f6f0284cb2a2a1108cf70e32750fb1edddf5c')
Children:
Parents:
1fe2271e3800804bd9a9bef62db37a53fa11b38e
Message:
```format

Location:
Singular/LIB
Files:
9 edited

Unmodified
Removed
• ## Singular/LIB/assprimeszerodim.lib

 r1fe227 { if(printlevel >= 9) { "size(L) = "+string(size(L)); } F = cleardenom(F[1]);

• ## Singular/LIB/involut.lib

 r1fe227 OVERVIEW: Involution is an anti-automorphism of a non-commutative K-algebra @* with the property that applied an involution twice, one gets an identity. @* Involution is linear with respect to the ground field. In this library we compute @* linear involutions, distinguishing the case of a diagonal matrix (such involutions @* are called homothetic) and a general one. Also, linear automorphisms of different @* order can be computed. with the property that applied an involution twice, one gets an identity. Involution is linear with respect to the ground field. In this library we compute linear involutions, distinguishing the case of a diagonal matrix (such involutions are called homothetic) and a general one. Also, linear automorphisms of different order can be computed. SUPPORT: Forschungsschwerpunkt 'Mathematik und Praxis' (Project of Dr. E. Zerz
• ## Singular/LIB/jacobson.lib

 r1fe227 OVERVIEW: We work over a ring R, that is an Euclidean principal ideal domain. @* If R is commutative, we suppose R to be a polynomial ring in one variable. @* If R is non-commutative, we suppose R to have two variables, say x and d. @* We treat then the basering as the Ore localization of R @* with respect to the mult. closed set S = K[x] without 0. @* Thus, we treat basering as principal ideal ring with d a polynomial @* variable and x an invertible one. @* Note, that in computations no division by x will actually happen. @* @* Given a rectangular matrix M over R, one can compute unimodular (that is @* invertible) square matrices U and V, such that U*M*V=D is a diagonal matrix. @* Depending on the ring, the diagonal entries of D have certain properties. @* @* We call a square matrix D as before 'a weak Jacobson normal form of M'. @* It is known, that over the first rational Weyl algebra K(x), D can be further @* transformed into a diagonal matrix (1,1,...,1,f,0,..,0), where f is in K(x). We call @* such a form of D the strong Jacobson normal form. The existence of strong form @* in not guaranteed if one works with algebra, which is not rational Weyl algebra. If R is commutative, we suppose R to be a polynomial ring in one variable. If R is non-commutative, we suppose R to have two variables, say x and d. We treat then the basering as the Ore localization of R with respect to the mult. closed set S = K[x] without 0. Thus, we treat basering as principal ideal ring with d a polynomial variable and x an invertible one. Note, that in computations no division by x will actually happen. Given a rectangular matrix M over R, one can compute unimodular (that is invertible) square matrices U and V, such that U*M*V=D is a diagonal matrix. Depending on the ring, the diagonal entries of D have certain properties. We call a square matrix D as before 'a weak Jacobson normal form of M'. It is known, that over the first rational Weyl algebra K(x), D can be further transformed into a diagonal matrix (1,1,...,1,f,0,..,0), where f is in K(x). We call such a form of D the strong Jacobson normal form. The existence of strong form in not guaranteed if one works with algebra, which is not rational Weyl algebra.
• ## Singular/LIB/modstd.lib

 r1fe227 //-------------------  Lift results to basering via farey  --------------------- tt = timer; tt = timer; N = T2[1]; for(i = 2; i <= size(T2); i++) { N = N*T2[i]; }
• ## Singular/LIB/nctools.lib

 r1fe227 A = embedMat(A,rB,cA); } else else { // rA>rB: add zero rows to B
• ## Singular/LIB/surf.lib

 r1fe227 /////////////////////////////////////////////////////////////////////////////// version="\$Id: surf.lib 13499 2010-10-15 09:55:26Z hannes \$"; version="\$Id\$"; category="Visualization"; info="
• ## Singular/LIB/surfacesignature.lib

 r1fe227 We have implemented three approaches using Puiseux expansions, the resolution of singularities resp. the spectral pairs of the singularity. REFERENCES:
• ## Singular/LIB/tropical.lib

 r1fe227 xc=substitute(bunchoflines[i][1]-cc,var(2),0,var(1),1); yc=substitute(bunchoflines[i][1]-cc,var(2),1,var(1),0); if (xc!=0) // then there is a point on the line with y-coordinate zero if (xc!=0) // then there is a point on the line with y-coordinate zero { gr[1]=-cc/leadcoef(xc); +(t0*r2*q1^2+s1*r0*r2*q1+s0*r2^2*q0)); poly a6=(-27*t0^2*q0^2+(9*t0*s0*r0-s0^3)*q0-t0*r0^3)*q3^2+ (((9*t0^2*q0-t0*s0*r0)*q1+((-3*t0*s0*r1+(3*t0*s1*r0+ 2*s1*s0^2))*q0+(t0*r0^2*r1-s1*s0*r0^2)))*q2+(-t0^2*q1^3 +(t0*s0*r1+(2*t0*s1*r0-s1*s0^2))*q1^2+((3*t0*s0*r2+ (-3*t0*s1*r1+2*s1^2*s0))*q0+((2*t0*r0^2-s0^2*r0)*r2+ (-t0*r0*r1^2+s1*s0*r0*r1-s1^2*r0^2)))*q1+((9*t0*s1*r2- s1^3)*q0^2+(((-3*t0*r0+s0^2)*r1-s1*s0*r0)*r2+(t0*r1^3 -s1*s0*r1^2+s1^2*r0*r1))*q0)))*q3+(-t0^2*q0*q2^3+ (-t0*s1*r0*q1+((2*t0*s0*r2+(t0*s1*r1-s1^2*s0))*q0- t0*r0^2*r2))*q2^2+(-t0*s0*r2*q1^2+(-t0*s1*r2*q0+ (t0*r0*r1-s1*s0*r0)*r2)*q1+((2*t0*r0-s0^2)*r2^2+ (-t0*r1^2+s1*s0*r1-s1^2*r0)*r2)*q0)*q2+ (-t0*r0*r2^2*q1^2+(t0*r1-s1*s0)*r2^2*q0*q1- (((9*t0^2*q0-t0*s0*r0)*q1+((-3*t0*s0*r1+(3*t0*s1*r0+ 2*s1*s0^2))*q0+(t0*r0^2*r1-s1*s0*r0^2)))*q2+(-t0^2*q1^3 +(t0*s0*r1+(2*t0*s1*r0-s1*s0^2))*q1^2+((3*t0*s0*r2+ (-3*t0*s1*r1+2*s1^2*s0))*q0+((2*t0*r0^2-s0^2*r0)*r2+ (-t0*r0*r1^2+s1*s0*r0*r1-s1^2*r0^2)))*q1+((9*t0*s1*r2- s1^3)*q0^2+(((-3*t0*r0+s0^2)*r1-s1*s0*r0)*r2+(t0*r1^3 -s1*s0*r1^2+s1^2*r0*r1))*q0)))*q3+(-t0^2*q0*q2^3+ (-t0*s1*r0*q1+((2*t0*s0*r2+(t0*s1*r1-s1^2*s0))*q0- t0*r0^2*r2))*q2^2+(-t0*s0*r2*q1^2+(-t0*s1*r2*q0+ (t0*r0*r1-s1*s0*r0)*r2)*q1+((2*t0*r0-s0^2)*r2^2+ (-t0*r1^2+s1*s0*r1-s1^2*r0)*r2)*q0)*q2+ (-t0*r0*r2^2*q1^2+(t0*r1-s1*s0)*r2^2*q0*q1- t0*r2^3*q0^2)); poly b2=a1^2+4*a2;
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