1-1. 최초 mylib 폴더 안에는 linalgcas.tns 와 numtheory.tns 라이브러리가 들어 있습니다. (이 댓글에 첨부합니다)
linalgcas library
TABLE OF CONTENTS
Part1: Linear Algebra
ceigenvals(Matrix)- symbolic complex eigenvalues of a matrix
clearmat()- delete temporary matrices
cofactor(Matrix,i,j) - cofactor of a matrix
comatrix(Matrix) - comatrix of a matrix (matrix of cofactors)
diagonalization(Matrix)- matrix diagonalization
dn(Matrix)- Jordan–Chevalley decomposition of a matrix M, where M=D+N, N·D=D·N
eigenvals(Matrix)- symbolic real eigenvalues of a matrix
eigenvects(Matrix,λ)- symbolic basis of the eigenspace of a matrix related to eigenvalue λ.
expmat(Matrix)- symbolic matrix exponential, ^(t·Matrix).
gausstep(Matrix)- step-by-step row matrix reduction.
help()- displays syntax info for functions and programs from library linalgcas.
inversestep(Matrix)- step-by-step matrix inverse computation.
kernelbasis(Matrix)- basis of kernel (null space) of a square matrix
kernelvectors(Matrix)- kernel (null space) vectors of a matrix
pwrmat(Matrix)- symbolic matrix power,Matrix^(n)
rank(Matrix)- rank of a matrix
simultstep(aMatrix, bVector)- step-by-step version of simult().
Part2: System of Linear Differential Equations
desystem(A,B)- solve system of differential equations in the form X'(t)=A·X(t)+B(t)
desysinitcond(A,B,t0,X0)- solve above system with initial condition X(t0)=x0.
desysnewcond(t1,X1)- solve the previously solved system of linear differential equations again, but with new initial conditions X(t1)=X1
numtheory library (en/fr/ge) - version 1.00 (2009-02-17)
Public functions for arithmetic
bezout(a,b) - (u,v,d)such that ua+bv=d, with d=gcd(a,b)
contfrac2real(list)- converts the continued fraction list to a real number
divisors(n)- list of divisors of n
factorstep(n)- step-by-step factorization of integer n
gcdstep(a,b)- step-by-step gcd
listprimediv(n)- list of prime divisors
nextprime(n)- first prime psuch that n≤p
phi(n)- number of positive integers not exceeding n and relatively prime to n
prevprime(n)- last prime psuch that p≤n
primecount(a,b)- counts the primes between aand b
primelist(a, b)- generates the list of primes between aand b
pwrmod(a,n,b)- compute a^(n) mod b(even for large values of aand n)
real2contfrac(num,k)- generates a list of the first k convergents for the continued fraction of a real number num.
Public functions for study of permutations
randperm(n)- generate a random permutation of {1,2,3,...,n}
signature(σ)- signature of a permutation defined by the list {σ(1),σ(2),...}
signaturestep(σ)- step-by-step signature of a permutation, with intermediate steps (with display of the decomposition in disjoint cycles)
Others tools included in this library
select(List,"boolean_expr(x)")- selects elements of a list with a specified property
select_range(n1,n2,"boolean_expr(x)")- selects integers elements between n1and n2with a specified property
sort_asc(ListNum)- sorts a list of numeric values in ascending order
sort_desc(ListNum)- sorts a list of numeric values in descending order
Private functions
These functions are not shown in the catalog, but they may however be used in other documents, if they are called by their long names.
numtheory\is_perm(List)- tests if a list does define a permutation: elements must be integers from 1 to n (number of elements of the list) and each must appear exactly once.
1-1. 최초 mylib 폴더 안에는 linalgcas.tns 와 numtheory.tns 라이브러리가 들어 있습니다. (이 댓글에 첨부합니다)
linalgcas library
TABLE OF CONTENTS
Part1: Linear Algebra
ceigenvals(Matrix)- symbolic complex eigenvalues of a matrix
clearmat()- delete temporary matrices
cofactor(Matrix,i,j) - cofactor of a matrix
comatrix(Matrix) - comatrix of a matrix (matrix of cofactors)
diagonalization(Matrix)- matrix diagonalization
dn(Matrix)- Jordan–Chevalley decomposition of a matrix M, where M=D+N, N·D=D·N
eigenvals(Matrix)- symbolic real eigenvalues of a matrix
eigenvects(Matrix,λ)- symbolic basis of the eigenspace of a matrix related to eigenvalue λ.
expmat(Matrix)- symbolic matrix exponential, ^(t·Matrix).
gausstep(Matrix)- step-by-step row matrix reduction.
help()- displays syntax info for functions and programs from library linalgcas.
inversestep(Matrix)- step-by-step matrix inverse computation.
kernelbasis(Matrix)- basis of kernel (null space) of a square matrix
kernelvectors(Matrix)- kernel (null space) vectors of a matrix
pwrmat(Matrix)- symbolic matrix power,Matrix^(n)
rank(Matrix)- rank of a matrix
simultstep(aMatrix, bVector)- step-by-step version of simult().
Part2: System of Linear Differential Equations
desystem(A,B)- solve system of differential equations in the form X'(t)=A·X(t)+B(t)
desysinitcond(A,B,t0,X0)- solve above system with initial condition X(t0)=x0.
desysnewcond(t1,X1)- solve the previously solved system of linear differential equations again, but with new initial conditions X(t1)=X1
numtheory library (en/fr/ge) - version 1.00 (2009-02-17)
Public functions for arithmetic
bezout(a,b) - (u,v,d)such that ua+bv=d, with d=gcd(a,b)
contfrac2real(list)- converts the continued fraction list to a real number
divisors(n)- list of divisors of n
factorstep(n)- step-by-step factorization of integer n
gcdstep(a,b)- step-by-step gcd
listprimediv(n)- list of prime divisors
nextprime(n)- first prime psuch that n≤p
phi(n)- number of positive integers not exceeding n and relatively prime to n
prevprime(n)- last prime psuch that p≤n
primecount(a,b)- counts the primes between aand b
primelist(a, b)- generates the list of primes between aand b
pwrmod(a,n,b)- compute a^(n) mod b(even for large values of aand n)
real2contfrac(num,k)- generates a list of the first k convergents for the continued fraction of a real number num.
Public functions for study of permutations
randperm(n)- generate a random permutation of {1,2,3,...,n}
signature(σ)- signature of a permutation defined by the list {σ(1),σ(2),...}
signaturestep(σ)- step-by-step signature of a permutation, with intermediate steps (with display of the decomposition in disjoint cycles)
Others tools included in this library
select(List,"boolean_expr(x)")- selects elements of a list with a specified property
select_range(n1,n2,"boolean_expr(x)")- selects integers elements between n1and n2with a specified property
sort_asc(ListNum)- sorts a list of numeric values in ascending order
sort_desc(ListNum)- sorts a list of numeric values in descending order
Private functions
These functions are not shown in the catalog, but they may however be used in other documents, if they are called by their long names.
numtheory\is_perm(List)- tests if a list does define a permutation: elements must be integers from 1 to n (number of elements of the list) and each must appear exactly once.