A B C D E F G H I L M N O P Q R S T U Z

A

a(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the first coefficient (element) of the matrix as an element of the base ring.
add(RingElt, RingElt) - Method in class com.perisic.ring.DoubleField
Addition.
add(RingElt, RingElt) - Method in class com.perisic.ring.F2Field
The addition a + b mod 2.
add(RingElt, RingElt) - Method in class com.perisic.ring.IntegerRing
Returns the sum of the parameters.
add(RingElt, RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the sum of a 2*2 matrix, m1 + m2.
add(RingElt, RingElt) - Method in class com.perisic.ring.ModularIntegerRing
Returns a + b mod m.
add(RingElt, RingElt) - Method in class com.perisic.ring.ModularRing
Addition.
add(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns the sum of the parameters.
add(RingElt, RingElt) - Method in class com.perisic.ring.QuotientField
Addition a + b.
add(RingElt, RingElt) - Method in class com.perisic.ring.RationalField
Returns a + b.
add(RingElt, RingElt) - Method in class com.perisic.ring.Ring
The addition a + b of two ring elements a and b.
add(RingElt, RingElt) - Method in class com.perisic.ring.UniversalRing
Addition.

B

b(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the second element of the matrix as an element of the base ring.

C

C - Static variable in class com.perisic.ring.Ring
The field C of complex numbers.
c(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the third element of the matrix as an element of the base ring.
construct(BigInteger, BigInteger) - Method in class com.perisic.ring.RationalField
Returns numerator/denominator.
construct(int[], Object[]) - Method in class com.perisic.ring.PolynomialRing
Returns a Polynomial by matching exponents to coefficients.
construct(int, Object) - Method in class com.perisic.ring.PolynomialRing
Returns the Polynomial coefficient * X^exponent, where X is the variable of this PolynomialRing.
construct(RingElt, RingElt) - Method in class com.perisic.ring.QuotientField
Constructs numerator/denominator.
construct(RingElt, RingElt, RingElt, RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
constructs the elements of a 2*2 matrix, a, b, c, and d.
contents(RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns the contents of b.
CyclotomicField - class com.perisic.ring.CyclotomicField.
This class implements a cyclotomic field.
CyclotomicField(int, String) - Constructor for class com.perisic.ring.CyclotomicField
Constructs the algebraic number field which contains all nth roots of unity.

D

d(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the fourth element of the matrix as an element of the base ring.
degree(RingElt) - Method in class com.perisic.ring.PolynomialRing
The degree of b, where b is considered as an univariate polynomial.
denominator(RingElt) - Method in class com.perisic.ring.QuotientField
Returns the denominator of b as an element of the base ring.
denominatorToBigInteger(RingElt) - Static method in class com.perisic.ring.RationalField
Returns the denominator s if b = r/s.
det(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the determinant of m.
displayMod() - Method in class com.perisic.ring.ModularRing
Determins the behaviour of the eltToString() method.
div(RingElt, RingElt) - Method in class com.perisic.ring.Ring
Computes a/b.
divmod(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns an array { p/q, p%q }.
DoubleField - class com.perisic.ring.DoubleField.
The real numbers.

E

ediv(RingElt, RingElt) - Method in class com.perisic.ring.IntegerRing
Euclidian division.
ediv(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns p/q (Euclidian division).
ediv(RingElt, RingElt) - Method in class com.perisic.ring.Ring
Returns a div b (euclidian division).
ediv(RingElt, RingElt) - Method in class com.perisic.ring.UniversalRing
Euclidian division.
eltToString(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the matrix m as a String.
eltToString(RingElt) - Method in class com.perisic.ring.ModularRing
Returns a in the form "a" or "a mod f" depending on the value of hideMod.
eltToString(RingElt) - Method in class com.perisic.ring.Ring
Returns the Ring element a as a String.
equal(RingElt, RingElt) - Method in class com.perisic.ring.Ring
True if a == b.
equals(Object) - Method in class com.perisic.ring.ModularIntegerRing
Two ModularIntegerRing objects are equal, if the modulus is the same.
equals(Object) - Method in class com.perisic.ring.PolynomialRing
true if coefficient ring and variable are the same.
equals(Object) - Method in class com.perisic.ring.RingElt
Equality is checked via the method equal() of the ring R to which the element belongs.
equalZero(RingElt) - Method in class com.perisic.ring.DoubleField
true if b == 0.
equalZero(RingElt) - Method in class com.perisic.ring.F2Field
Returns true if a == 0.
equalZero(RingElt) - Method in class com.perisic.ring.IntegerRing
Returns true if b is equals to zero, false otherwise.
equalZero(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns true if the matrix m1 == 0.
equalZero(RingElt) - Method in class com.perisic.ring.ModularIntegerRing
True if b == 0, false otherwise.
equalZero(RingElt) - Method in class com.perisic.ring.ModularRing
true if b == 0, false otherwise.
equalZero(RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns true if b is equals to zero, false otherwise.
equalZero(RingElt) - Method in class com.perisic.ring.QuotientField
True if b == 0.
equalZero(RingElt) - Method in class com.perisic.ring.RationalField
True if b == 0.
equalZero(RingElt) - Method in class com.perisic.ring.Ring
Returns true if a == 0.
equalZero(RingElt) - Method in class com.perisic.ring.UniversalRing
true if b == 0.
evaluatePolynomial(RingElt, RingElt) - Method in class com.perisic.ring.Ring
Evaluates the Polynomial p at b.
extendedGcd(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Extended greatest common divisor of the parameters.

F

F2 - Static variable in class com.perisic.ring.F2Field
The field F2.
F2 - Static variable in class com.perisic.ring.Ring
The field F2 of integers modulo 2.
F2Field - class com.perisic.ring.F2Field.
The finite prime field of characteristic 2.
findRing() - Method in class com.perisic.ring.UniversalCyclotomicField
 
findRing() - Method in class com.perisic.ring.UniversalPolynomialRing
 
findRing() - Method in class com.perisic.ring.UniversalRing
A suitable ring able to map 0 (and 1).
findRing(RingElt) - Method in class com.perisic.ring.UniversalCyclotomicField
Returns the ring of the argument a if this a Cyclotomic field or Q.
findRing(RingElt) - Method in class com.perisic.ring.UniversalPolynomialRing
The ring over the coefficient ring with the variables of a.getRing().
findRing(RingElt) - Method in class com.perisic.ring.UniversalRing
A suitable ring able to map a.
findRing(RingElt, RingElt) - Method in class com.perisic.ring.UniversalCyclotomicField
Returns cyaclotomic field which contains both a and b.
findRing(RingElt, RingElt) - Method in class com.perisic.ring.UniversalPolynomialRing
The result is the coefficient ring over the variables of a.getRing() and the variables of b.getRing().
findRing(RingElt, RingElt) - Method in class com.perisic.ring.UniversalRing
A suitable ring able to map a and b.
FinitePrimeField - class com.perisic.ring.FinitePrimeField.
Title: FinitePrimeField
FinitePrimeField(int) - Constructor for class com.perisic.ring.FinitePrimeField
Generates a finite prime field of characteristic m.
FinitePrimeField(Object) - Constructor for class com.perisic.ring.FinitePrimeField
Generates a finite prime field of characteristic modulus.

G

gcd(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Greatest common divisor of the parameters.
gcd(RingElt, RingElt) - Method in class com.perisic.ring.Ring
Returns gcd(a,b).
gcd(RingElt, RingElt) - Method in class com.perisic.ring.UniversalRing
gcd.
getbaseRing() - Method in class com.perisic.ring.Matrix2x2Ring
Returns the ring of coefficients of the matrix.
getBaseRing() - Method in class com.perisic.ring.QuotientField
Returns the denominator and numerator ring B (the base ring).
getCoefficientAt(int, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns the coefficient for x^i of b (or null), where b is considered as an univariate polynomial over x.
getCoefficientRing() - Method in class com.perisic.ring.PolynomialRing
Returns the Ring R sucht that the PolynomialRing is the Ring R[x] where x is the variable of the PolynomialRing.
getCyclotomicPolynomial(Ring, int, String) - Static method in class com.perisic.ring.CyclotomicField
Constructs the n-th cyclotomic polynomial over the ring F as a polynomial in the variable variable.
getHideMod() - Method in class com.perisic.ring.ModularRing
true if hideMod() has been called.
getMatrixFormat() - Method in class com.perisic.ring.Matrix2x2Ring
returns the format of the matrices.
getModulus() - Method in class com.perisic.ring.ModularIntegerRing
Returns m where this ModularIntegerRing is Z/mZ.
getModulus() - Method in class com.perisic.ring.ModularRing
Returns f if this is R/fR.
getN() - Method in class com.perisic.ring.CyclotomicField
returns the n if this is the nth cyclotomic field
getRing() - Method in class com.perisic.ring.RingElt
Returns the ring R which has been used for construction of the element.
getTrueCoefficientAt(int, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns the coefficient for x^i of b, where b is considered as an univariate polynomial over x.
getValue(RingElt) - Method in class com.perisic.ring.ModularRing
Returns the value of b as an element of R.
getVariable() - Method in class com.perisic.ring.PolynomialRing
Returns the variable x sucht that the PolynomialRing is the Ring R[x] where R is a Ring.
globalLeadingCoefficient(RingElt) - Method in class com.perisic.ring.PolynomialRing
Determins recursively the global leading Coefficient of the polynomial over all variables.

H

hideMod() - Method in class com.perisic.ring.ModularRing
Determins the behaviour of the eltToString() method.

I

IntegerRing - class com.perisic.ring.IntegerRing.
The ring of Integers.
inv(RingElt) - Method in class com.perisic.ring.DoubleField
Multiplicative Inverse.
inv(RingElt) - Method in class com.perisic.ring.F2Field
Returns b^-1.
inv(RingElt) - Method in class com.perisic.ring.IntegerRing
Returns b for b == 1 and b == -1.
inv(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the inverse of a matrix m1.
inv(RingElt) - Method in class com.perisic.ring.ModularIntegerRing
Returns b^-1 mod m.
inv(RingElt) - Method in class com.perisic.ring.ModularRing
Returns the inverse b.
inv(RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns 1/b as an element of this Ring.
inv(RingElt) - Method in class com.perisic.ring.QuotientField
Returns b^-1.
inv(RingElt) - Method in class com.perisic.ring.RationalField
Returns the multiplicative inverse.
inv(RingElt) - Method in class com.perisic.ring.Ring
Returns b^-1.
inv(RingElt) - Method in class com.perisic.ring.UniversalRing
Multiplicative Inverse.
isEuclidian() - Method in class com.perisic.ring.IntegerRing
Returns true as Z is an Euclidian ring.
isEuclidian() - Method in class com.perisic.ring.PolynomialRing
true if the coefficient ring is a field.
isEuclidian() - Method in class com.perisic.ring.Ring
Is the ring Euclidian? By default false.
isField() - Method in class com.perisic.ring.CyclotomicField
returns true.
isField() - Method in class com.perisic.ring.DoubleField
Returns true.
isField() - Method in class com.perisic.ring.F2Field
 
isField() - Method in class com.perisic.ring.FinitePrimeField
returns true.
isField() - Method in class com.perisic.ring.Matrix2x2Ring
Returns false.
isField() - Method in class com.perisic.ring.QuotientField
Returns true.
isField() - Method in class com.perisic.ring.RationalField
Returns true.
isField() - Method in class com.perisic.ring.Ring
Is the ring a field? By default false.
isField() - Method in class com.perisic.ring.UniversalCyclotomicField
returns true, as this is a field.
isIntegral(RingElt) - Method in class com.perisic.ring.QuotientField
true if the denominator is one.
isIntegral(RingElt) - Static method in class com.perisic.ring.RationalField
true if denominator of b equals 1.
isUFD() - Method in class com.perisic.ring.PolynomialRing
true if the coefficient ring and therefore also the polynomial ring is an uniqe factorization domain.
isUFD() - Method in class com.perisic.ring.Ring
Is the ring a UFD (unique factorization domain)? By default false.
isUFD() - Method in class com.perisic.ring.UniversalPolynomialRing
true if the coefficient ring and therefore also the polynomial ring is an uniqe factorization domain.

L

leadingCoefficient(RingElt) - Method in class com.perisic.ring.PolynomialRing
The leading coefficient of b, where b is considered as an univariate polynomial.

M

main(String[]) - Static method in class com.perisic.ring.CyclotomicField
A very simple tester for this class.
main(String[]) - Static method in class com.perisic.ring.Matrix2x2Ring
A simple test method.
main(String[]) - Static method in class com.perisic.ring.QuotientField
 
main(String[]) - Static method in class com.perisic.ring.UniversalCyclotomicField
This is for testing this class only.
main(String[]) - Static method in class com.perisic.ring.UniversalPolynomialRing
 
map(BigInteger) - Method in class com.perisic.ring.Ring
Maps a into the Ring.
map(boolean) - Method in class com.perisic.ring.F2Field
Maps false to 0 and true to 1.
map(double) - Method in class com.perisic.ring.DoubleField
Maps a double to this field.
map(int) - Method in class com.perisic.ring.Ring
Maps a into the Ring.
map(int, String) - Method in class com.perisic.ring.UniversalCyclotomicField
maps the string str into the n-th cyclotomic field
map(Object) - Method in class com.perisic.ring.Ring
By default, maps a into the Ring using appropriate methods if a is a RingElt, a BigInteger or a String.
map(RingElt) - Method in class com.perisic.ring.CyclotomicField
If the ring of the argument is of a dth cyclotomic field and d a divisor of n we embed via the mapping zd -> znn/d where zn denotes a fixed nth root of unity.
map(RingElt) - Method in class com.perisic.ring.F2Field
If b is a modular integer ring, such that the modulus maps to 0, the value of b is mapped to F2.
map(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Maps a 2x2 matrix m into this.
map(RingElt) - Method in class com.perisic.ring.ModularIntegerRing
Performs the ususal map as in Ring.map(RingElt).
map(RingElt) - Method in class com.perisic.ring.ModularRing
If the ring of a is a quotient field we map the quotient of numerator and denominator.
map(RingElt) - Method in class com.perisic.ring.PolynomialRing
Maps a RingElt of various other rings to this ring.
map(RingElt) - Method in class com.perisic.ring.QuotientField
If a is an element of another QuotientRing, numerator and denominator are mapped to B.
map(RingElt) - Method in class com.perisic.ring.RationalField
Maps Ring.Z elements and into this.
map(RingElt) - Method in class com.perisic.ring.Ring
Maps a into the Ring.
map(RingElt) - Method in class com.perisic.ring.UniversalCyclotomicField
The following Rings are mapped: Cyclotomic fields, where the variable is of the form z* where z ist the preifx of the variable and * is a number; Polynomial rings and Quotient fields over Polynomial rings where the variables are of the form z*; the usual suspects (Z, Q).
map(RingElt) - Method in class com.perisic.ring.UniversalRing
Maps a RingElt using the findRing() method with one parameter.
map(String) - Method in class com.perisic.ring.DoubleField
Returns str as a DoubleField.
map(String) - Method in class com.perisic.ring.Matrix2x2Ring
Maps a matrix of the form { { xxx, yyy } { uuu, vvv } } into this ring.
map(String) - Method in class com.perisic.ring.ModularRing
Maps str first into R, then into this.
map(String) - Method in class com.perisic.ring.PolynomialRing
Maps a String to an element of this PolynomialRing.
map(String) - Method in class com.perisic.ring.QuotientField
Maps the String a into this Ring.
map(String) - Method in class com.perisic.ring.RationalField
Maps the String a of the form xxxxx/yyyyy and xxxxxx into this field.
map(String) - Method in class com.perisic.ring.Ring
Maps a String into the Ring.
map(String) - Method in class com.perisic.ring.UniversalCyclotomicField
Strings denoting Rational functions (elements of Quotient fields of Polynomial rings) over variables of the form z* where z ist the preifx of the variable and * is a number; are mapped.
map(String) - Method in class com.perisic.ring.UniversalPolynomialRing
All Java identifiers are allowed as variables.
map(String) - Method in class com.perisic.ring.UniversalRing
Maps a string to the ring obtained by findRing() without parameter.
Matrix2x2Ring - class com.perisic.ring.Matrix2x2Ring.
The ring of 2 x 2 matrices {{a,b},{c,d}} with a,b,c and d in B, where B is any Ring.
Matrix2x2Ring(Ring) - Constructor for class com.perisic.ring.Matrix2x2Ring
construction of a new Matrix2x2Ring over B.
mod(RingElt, RingElt) - Method in class com.perisic.ring.IntegerRing
Remainder of Euclidian division.
mod(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns p%q (remainder of Euclidian division).
mod(RingElt, RingElt) - Method in class com.perisic.ring.Ring
Returns a % m (euclidian division, a modulo m).
mod(RingElt, RingElt) - Method in class com.perisic.ring.UniversalRing
Modular computation.
ModularIntegerRing - class com.perisic.ring.ModularIntegerRing.
The modular integer ring Z/nZ.
ModularIntegerRing(int) - Constructor for class com.perisic.ring.ModularIntegerRing
 
ModularIntegerRing(Object) - Constructor for class com.perisic.ring.ModularIntegerRing
Construction of Z/mZ with m = modulus.
ModularRing - class com.perisic.ring.ModularRing.
Implements a ring R/fR where R is an element of the ring R.
ModularRing(RingElt) - Constructor for class com.perisic.ring.ModularRing
Constructs m.getRing()/m * m.getRing().
mult(RingElt, RingElt) - Method in class com.perisic.ring.DoubleField
Multiplication.
mult(RingElt, RingElt) - Method in class com.perisic.ring.F2Field
The multiplicaton a * b mod 2.
mult(RingElt, RingElt) - Method in class com.perisic.ring.IntegerRing
Returns the product of the parameters.
mult(RingElt, RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Return the product of two 2*2 matrices, m1 * m2.
mult(RingElt, RingElt) - Method in class com.perisic.ring.ModularIntegerRing
Returns a * b mod m.
mult(RingElt, RingElt) - Method in class com.perisic.ring.ModularRing
Multiplication.
mult(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns the product of the parameters.
mult(RingElt, RingElt) - Method in class com.perisic.ring.QuotientField
Multiplication a * b.
mult(RingElt, RingElt) - Method in class com.perisic.ring.RationalField
Returns a * b.
mult(RingElt, RingElt) - Method in class com.perisic.ring.Ring
The mutiplicaton a * b of two ring elements a and b.
mult(RingElt, RingElt) - Method in class com.perisic.ring.UniversalRing
Multiplication.

N

neg(RingElt) - Method in class com.perisic.ring.DoubleField
The additive inverse of b.
neg(RingElt) - Method in class com.perisic.ring.F2Field
Returns -a mod 2.
neg(RingElt) - Method in class com.perisic.ring.IntegerRing
Returns -b as an element of this Ring.
neg(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the negation of a matrix, -m1.
neg(RingElt) - Method in class com.perisic.ring.ModularIntegerRing
Returns -b mod m.
neg(RingElt) - Method in class com.perisic.ring.ModularRing
Returns -b.
neg(RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns -b as an element of this Ring.
neg(RingElt) - Method in class com.perisic.ring.QuotientField
Returns -b.
neg(RingElt) - Method in class com.perisic.ring.RationalField
Returns -b.
neg(RingElt) - Method in class com.perisic.ring.Ring
Returns the additive inverse -a of an ring element a.
neg(RingElt) - Method in class com.perisic.ring.UniversalRing
The additive inverse of b.
normalize(RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns a normal form for the polynomial b.
numerator(RingElt) - Method in class com.perisic.ring.QuotientField
Returns the numerator of b as an element of the base ring.
numeratorToBigInteger(RingElt) - Static method in class com.perisic.ring.RationalField
Returns the numerator r if b = r/s.

O

one() - Method in class com.perisic.ring.DoubleField
The 1 of the field.
one() - Method in class com.perisic.ring.F2Field
Returns the 1 of the ring.
one() - Method in class com.perisic.ring.IntegerRing
Returns 1 as an element of this Ring.
one() - Method in class com.perisic.ring.Matrix2x2Ring
Returns the Identity matrix, I = {{ 1, 0 } { 0, 1}}.
one() - Method in class com.perisic.ring.ModularIntegerRing
Returns 1.
one() - Method in class com.perisic.ring.ModularRing
Returns 1.
one() - Method in class com.perisic.ring.PolynomialRing
Returns 1 as an element of this Ring.
one() - Method in class com.perisic.ring.QuotientField
Returns 1.
one() - Method in class com.perisic.ring.RationalField
Returns 1.
one() - Method in class com.perisic.ring.Ring
Returns the 1 of the ring.
one() - Method in class com.perisic.ring.UniversalRing
The 1 of the ring.

P

PolynomialRing - class com.perisic.ring.PolynomialRing.
Multivariate Polynomials over a Ring.
PolynomialRing(Ring, String) - Constructor for class com.perisic.ring.PolynomialRing
Constructs a new polynomial ring over one or more variables.
PolynomialRing(Ring, String[]) - Constructor for class com.perisic.ring.PolynomialRing
Constructs a new polynomial ring over variables.length variables.
pow(RingElt, BigInteger) - Method in class com.perisic.ring.Ring
Returns b^a.
pow(RingElt, int) - Method in class com.perisic.ring.Ring
Returns b^a.
primitivePart(RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns b/contents(b).

Q

Q - Static variable in class com.perisic.ring.Ring
The field Q of fractions.
QuotientField - class com.perisic.ring.QuotientField.
A field of fractions p/q with p,q in B, where B is any Ring.
QuotientField(Ring) - Constructor for class com.perisic.ring.QuotientField
Construction.

R

R - Static variable in class com.perisic.ring.DoubleField
 
R - Static variable in class com.perisic.ring.Ring
The field R of real numbers.
RationalField - class com.perisic.ring.RationalField.
The field Q of rational numbers.
Ring - class com.perisic.ring.Ring.
Title: Ring
Ring() - Constructor for class com.perisic.ring.Ring
 
RingElt - class com.perisic.ring.RingElt.
This abstract class is the base class for all elements of concrete rings.
RingElt(Ring) - Constructor for class com.perisic.ring.RingElt
Constructs the ring element as an element of the ring R.
RingException - exception com.perisic.ring.RingException.
The exception class for all errors.
RingException(String) - Constructor for class com.perisic.ring.RingException
Construction.

S

setHideMod(boolean) - Method in class com.perisic.ring.ModularRing
Determins the behaviour of the eltToString() method.
setMatrixFormat(String, String, String, String, String) - Method in class com.perisic.ring.Matrix2x2Ring
Sets the format that is used to read and write matrices.
sub(RingElt, RingElt) - Method in class com.perisic.ring.Ring
Returns a - b.

T

tdiv(RingElt, RingElt) - Method in class com.perisic.ring.IntegerRing
True division.
tdiv(RingElt, RingElt) - Method in class com.perisic.ring.ModularIntegerRing
The same as div(a,b).
tdiv(RingElt, RingElt) - Method in class com.perisic.ring.PolynomialRing
Returns p/q (true division).
tdiv(RingElt, RingElt) - Method in class com.perisic.ring.Ring
Computes a/b (true division).
tdiv(RingElt, RingElt) - Method in class com.perisic.ring.UniversalRing
True division.
toBigInteger(RingElt) - Static method in class com.perisic.ring.IntegerRing
Returns the value of b as a BigInteger.
toBigInteger(RingElt) - Static method in class com.perisic.ring.ModularIntegerRing
Returns the BigInteger value of b.
toBoolean(RingElt) - Method in class com.perisic.ring.F2Field
Returns the boolean value of a.
toDouble(RingElt) - Static method in class com.perisic.ring.DoubleField
returns the double value of b.
toString() - Method in class com.perisic.ring.CyclotomicField
returns CYC(n).
toString() - Method in class com.perisic.ring.DoubleField
 
toString() - Method in class com.perisic.ring.F2Field
Returns the String "F2".
toString() - Method in class com.perisic.ring.IntegerRing
Returns "Z".
toString() - Method in class com.perisic.ring.Matrix2x2Ring
Returns M22(B) where B is the coefficient ring.
toString() - Method in class com.perisic.ring.PolynomialRing
Returns a the polynomial ring in the format R[x1][x2]...[xn].
toString() - Method in class com.perisic.ring.QuotientField
Returns "Quot(str)" where str = B.toString().
toString() - Method in class com.perisic.ring.RationalField
Returns "Q".
toString() - Method in class com.perisic.ring.RingElt
The String is found using the eltToString() method of the ring to which the element belongs.
toString() - Method in class com.perisic.ring.UniversalCyclotomicField
 
toString() - Method in class com.perisic.ring.UniversalPolynomialRing
 
toString() - Method in class com.perisic.ring.UniversalRing
 
trace(RingElt) - Method in class com.perisic.ring.Matrix2x2Ring
Returns the trace of m.

U

UniversalCyclotomicField - class com.perisic.ring.UniversalCyclotomicField.
The infinite algebraic extension of Q which contains all unit roots.
UniversalCyclotomicField(String) - Constructor for class com.perisic.ring.UniversalCyclotomicField
Construct the universal cyclotomic field by the prefix for the variable.
UniversalPolynomialRing - class com.perisic.ring.UniversalPolynomialRing.
The field of polynomials over all allowed variable names as variables.
UniversalPolynomialRing(Ring) - Constructor for class com.perisic.ring.UniversalPolynomialRing
Construct the universal polynomial field by the ring of coefficients.
UniversalRing - class com.perisic.ring.UniversalRing.
An abstract class for an universal ring.
UniversalRing() - Constructor for class com.perisic.ring.UniversalRing
No parameters in the constructor

Z

Z - Static variable in class com.perisic.ring.Ring
The ring Z of integers.
zero() - Method in class com.perisic.ring.DoubleField
The 0 of the field.
zero() - Method in class com.perisic.ring.F2Field
Returns 0 mod 2.
zero() - Method in class com.perisic.ring.IntegerRing
Returns 0 as an element of this Ring.
zero() - Method in class com.perisic.ring.Matrix2x2Ring
Returns the zero matrix { { 0, 0 } { 0, 0 }}.
zero() - Method in class com.perisic.ring.ModularIntegerRing
Returns 0.
zero() - Method in class com.perisic.ring.ModularRing
Returns 0.
zero() - Method in class com.perisic.ring.PolynomialRing
Returns 0 as an element of this Ring.
zero() - Method in class com.perisic.ring.QuotientField
Returns 0.
zero() - Method in class com.perisic.ring.RationalField
Returns 0.
zero() - Method in class com.perisic.ring.Ring
Returns the 0 of the ring.
zero() - Method in class com.perisic.ring.UniversalRing
The 0 of the ring.

A B C D E F G H I L M N O P Q R S T U Z