term(3) UNIX System V (Nov 25, 1998) term(3)
Term
Inherits from:
CAObject
Class Description
Maturity Index : Relatively Mature
A term consists of a coefficient multiplied by a symbol
raised to an integral exponent . The coefficient is a
scalar object or a polynomial. The symbol object is nil if
the exponent is equal to zero.
Recursive Polynomials
A polynomial in recursive representation is a sum of terms.
If the polynomial is variable sparse, each symbol can be
different and the coefficients of the terms are scalar
objects or again variable sparse polynomials; if the
coefficient is not a scalar object, then the exponent of the
term cannot be zero (for example, the term 3 x ^0 y ^2 z ^0
is reduced to 3 y ^2 in the variable sparse case). If the
polynomial is variable dense, all symbols are equal to each
other and the coefficients are either all scalar objects or
again all variable dense polynomials; the exponent of a term
may be zero, even if the coefficient is a polynomial (3 x ^0
y ^2 z ^0 is a valid object in the variable dense case). In
a degree dense polynomial, the coefficients of the terms can
be zero; in a degree sparse polynomial they cannot.
Monomials
A monomial is a product of terms. The coefficients of the
terms of a monomial are scalar objects that are equal to one
(but it's possible to insert terms with a non-trivial
coefficient). In a variable dense monomial, the exponents
of the terms can be equal to zero; in a variable sparse
monomial, they cannot.
Factors
A factored polynomial is a product of terms. The
coefficients of the terms in the factorization are scalar
objects, mostly equal to one, but they can store the content
extracted out of the (primitive) factors. The symbol
(nucleus) objects of the terms are polynomials i.e., the
factors in the factorization.
Method types
Creation
* scalar:symbol:exponent:
* coefficient:symbol:exponent:
* copy
* deepCopy
* clear
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Identity
* scalarZero
* coefficient
* symbol
* exponent
* degree
* hash
* isEqual:
* compareExponents:
Coercion
* intValue
* intValue:
* floatValue
* floatValue:
* asScalar
* asSymbol
Addition
* zero
* isZero
* isOpposite:
* negate
* double
* add:
* subtract:
Multiplication
* one
* isOne
* isMinusOne
* square
* inverse
* multiplyScalar:
* multiplyCoefficient:
* multiply:
* divideScalar:
* divideCoefficient:
* divide:
Exponentation
* power:
* root:
* squareRoot
Characteristic
* frobenius
* frobeniusInverse
Derivation and Integration
* derive
* integrate
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Printing
* printsLeadingSign
* printsSum
* printsProduct
* printOn:
Methods
scalar:symbol:exponent:
+ scalar : aScalar symbol : aSymbol exponent :(int)
anExponent
Creates a new term with coefficient, symbol and exponent set
to the specified objects. This method sets scalarZero to
the zero element for aScalar .
coefficient:symbol:exponent:
+ coefficient : aCoefficient symbol : aSymbol exponent
:(int) anExponent
Creates a new term with coefficient, symbol and exponent set
to the specified objects. This method sets scalarZero to
the zero element obtained by sending scalarZero to
aCoefficient .
copy
- copy
Copies the term object, and if the coefficient is a scalar
object, adds a reference to it. If the coefficient is a
polynomial, makes a copy of it.
See also:
copy (Polynomial)
deepCopy
- deepCopy
Makes deep copies of the term object and its coefficient and
symbol.
See also:
deepCopy (Polynomial)
clear
- clear
Frees coefficient and symbol (if non-nil).
scalarZero
- scalarZero
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Returns the zero scalar of the term; you may not modify or
free this object.
coefficient
- coefficient
Returns the coefficient of the term; you may not modify or
free this object.
symbol
- symbol
Returns the symbol of the term; you may not modify or free
this object. If the exponent of the term is equal to zero,
this method returns nil .
exponent
- ( int ) exponent
Returns the exponent of the term. If the exponent is equal
to zero, the symbol of the term is equal to nil .
degree
- ( int ) degree
Equivalent to exponent .
hash
- ( unsigned ) hash
Returns a small integer that is the same for terms that are
equal (in the sense of isEqual: ).
isEqual:
- ( BOOL ) isEqual : b
Two terms are equal if they are pointer equal or if the
coefficients are equal, if the exponents are equal and if
the symbols are equal (or both nil ).
compareExponents:
- ( int ) compareExponents : b
Compares two terms with respect to symbols and exponents;
this imposes an ordering for the terms in variable sparse
polynomials. Returns zero if the terms are pointer equal.
A term with symbol nil is less than a term with non-nil
symbol. Compares the symbols, and if they are equal,
compares the exponents.
intValue
- ( int ) intValue
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Returns, if the exponent is equal to zero, the intValue of
the coefficient. If not, generates an error message.
intValue:
- intValue :(int) aValue
Returns a new term with exponent equal to zero and with a
coefficient whose value as int is equal to aValue .
floatValue
- ( float ) floatValue
Returns, if the exponent is equal to zero, the floatValue of
the coefficient. If not, generates an error message.
floatValue:
- floatValue :(float) aValue
Returns a term with exponent equal to zero and with a
coefficient whose value as float is equal to aValue .
asScalar
- asScalar
Returns the term as scalar object. Returns nil if the
exponent of the term is not equal to zero. If the
coefficient of the term is a scalar, the method returns a
new reference to it, otherwise the coefficient is a
polynomial and the method returns the scalar value of it.
Note that in the variable sparse case, a term that is a
scalar must have a scalar object as coefficient i.e., the
term is always simplified.
asSymbol
- asSymbol
Returns the term as symbol object. If the exponent of the
term is zero and if the coefficient is a polynomial, returns
the symbol value of the polynomial. If the exponent is
equal to one and the coefficient is one, returns a new
reference to the symbol of the term. Otherwise returns nil
.
zero
- zero
Returns a new term with coefficient equal to the zero
element for the coefficient of the term that receives the
message.
isZero
- ( BOOL ) isZero
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Whether the coefficient of the term is equal to zero. The
exponent of the term may be non-zero.
isOpposite:
- ( BOOL ) isOpposite : b
Whether the coefficients of the term are opposite, and the
exponents and symbols are equal to each other.
negate
- negate
Negates the coefficient of the term.
double
- double
Doubles the coefficient of the term.
add:
- add : b
Returns a new term that is the sum of the two terms i.e.,
the coefficients are added together using add: or
addScalar: . The exponents must be equal and the symbols
must be both nil or equal to each other.
subtract:
- subtract : b
Returns a new term that is the difference of the two terms
i.e., the coefficients are subtracted from each other using
subtract: or subtractScalar: . The exponents must be
equal and the symbols must be both nil or equal to each
other.
one
- one
Returns a term with coefficient equal to one.
isOne
- ( BOOL ) isOne
Whether the coefficient is one and the exponent is equal to
zero.
isMinusOne
- ( BOOL ) isMinusOne
Whether the coefficient is minus one and the exponent is
equal to zero.
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square
- square
Squares coefficient and multiplies exponent by two.
inverse
- inverse
Inverts coefficient and negates the exponent. Returns nil
if the coefficient has no inverse.
multiplyScalar:
- multiplyScalar : b
Returns a new term; multiplies the coefficient of the term
by the scalar object b , using multiply: if the coefficient
of the term is a scalar object, or multiplyScalar:
otherwise. The symbol and exponent of the resulting term
are equal to that of the original term.
multiplyCoefficient:
- multiplyCoefficient : b
Returns a new term; multiplies the coefficient of the term
by the coefficient object b , which must be an instance of
the same class as the coefficient of the term. The symbol
and exponent of the resulting term are equal to that of the
original term. The method is implemented only for terms of
variable dense (recursive) polynomials.
multiply:
- multiply : b
Returns a new term that is the product of the two terms
i.e., the exponents are added together and the coefficients
are multiplied using multiply: or multiplyScalar: . If
the exponents are both non-zero, then the symbols must be
equal to each other. If one of the terms has exponent equal
to zero, then the symbol of the resulting term is equal to
that of the term with non-zero exponent.
divideScalar:
- divideScalar : b
Returns a new term; divides the coefficient of the term by
the scalar object b , using divide: if the coefficient of
the term is a scalar object, or divideScalar: otherwise.
The symbol and exponent of the resulting term are equal to
that of the original term. Returns nil if the scalar
division is not exact.
divideCoefficient:
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- divideCoefficient : b
Returns a new term; divides the coefficient of the term by
the object b , which is an instance of the same class as the
coefficient. The symbol and exponent of the resulting term
are equal to that of the original term. Returns nil if the
division is not exact. The method is implemented only for
terms of a variable dense polynomial.
divide:
- divide : b
Returns a new term that is the exact quotient of the two
terms i.e., the exponents are subtracted from each other and
the coefficients are divided using divide: or divideScalar:
. If the exponents are both non-zero, then the symbols must
be equal to each other. If one of the terms has exponent
equal to zero, then the symbol of the resulting term is
equal to that of the term with non-zero exponent. Returns
nil if the exponent of the divisor is greater than that of
the dividend, or if the coefficient division fails.
power:
- power :(int) n
Raises coefficient to the n -th power and multiplies
exponent by n .
root:
- root :(int) n
Takes the n -th root of the coefficient and divides exponent
by n . Returns nil if the coefficient is not an n -th power
or if the exponent is not divisible by n .
squareRoot
- squareRoot
Takes the square root of the coefficient and divides
exponent by two. Returns nil if the coefficient is not a
square or if the exponent is not divisible by two.
frobenius
- frobenius
Returns the p -th power of the term, obtained by raising the
term to a power equal to the characteric of the coefficient.
frobeniusInverse
- frobeniusInverse
Returns either nil (if the term is not a p -th power) or a
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new term that is the p -th root of the term.
derive
- derive
Returns the derivative with respect to the variable.
integrate
- integrate
Integrates with respect to the variable.
printsLeadingSign
- ( BOOL ) printsLeadingSign
Whether the term prints a leading minus sign.
printsSum
- ( BOOL ) printsSum
Whether the term prints a sum.
printsProduct
- ( BOOL ) printsProduct
Whether the term prints a single product.
printOn:
- printOn :(IOD) aFile
Prints, between braces, a comma separated list of the
members. If there are no members, the method prints two
braces.
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