Ops.spray
Arithmetic Ops Group Methods for sprays
Allows arithmetic operators to be used for spray calculations, such as addition, multiplication, division, integer powers, etc. Objects of class spray are interpreted as sparse multivariate polynomials.
- Keywords
- symbolmath
Usage
# S3 method for spray
Ops(e1, e2 = NULL)
spray_negative(S)
spray_times_spray(S1,S2)
spray_times_scalar(S,x)
spray_plus_spray(S1,S2)
spray_plus_scalar(S,x)
spray_power_scalar(S,n)
spray_eq_spray(S1,S2)Arguments
- e1,e2,S,S1,S2
Objects of class spray, here interpreted as sparse multivariate polynomials
- x
Real valued scalar
- n
Non-negative integer
Details
The function Ops.spray() passes unary and binary arithmetic
operators (“+”, “-”, “*”,
“/”,“==”, and “^”) to the
appropriate specialist function.
The most interesting operators are “*” and
“+” which execute multivariate polynomial multiplication
and addition respectively.
Testing for equality uses spray_eq_spray(). Note that
spray_eq_spray(S1,S2) is algebraically equivalent to
is.zero(S1-S2), but faster (FALSE is returned as soon as
a mismatch is found).
Value
The functions all return spray objects except “==”, which
returns a logical.
Note
Notes here
See Also
Examples
# NOT RUN {
M <- matrix(sample(0:3,21,replace=TRUE),ncol=3)
a <- spray(M,sample(7))
b <- homog(3,4)
# arithmetic operators mostly work as expected:
a + 2*b
a - a*b^2/4
a+b
S1 <- spray(partitions::compositions(4,3))
S2 <- spray(diag(3)) # S2 = x+y+z
stopifnot( (S1+S2)^3 == S1^3 + 3*S1^2*S2 + 3*S1*S2^2 + S2^3 )
# }