Description Usage Arguments Details Author(s) Examples

Arithmetic operators for manipulation of freealg objects such as addition, multiplication, powers, etc

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## S3 method for class 'freealg'
Ops(e1, e2)
free_negative(S)
free_power_scalar(S,n)
free_eq_free(e1,e2)
free_plus_numeric(S,x)
free_plus_free(e1,e2)
lowlevel_simplify(words,coeffs)
lowlevel_free_prod(words1,coeffs1,words2,coeffs2)
lowlevel_free_sum(words1,coeffs1,words2,coeffs2)
lowlevel_free_power(words,coeffs,n)
lowlevel_diffn(words,coeffs,r)
lowlevel_subs(words1, coeffs1, words2, coeffs2, r)
``` |

`S,e1,e2` |
Objects of class |

`n` |
Integer, possibly non-positive |

`r` |
Integer vector indicating variables to differentiate with respect to |

`x` |
Scalar value |

`words,words1,words2` |
A list of words, that is, a list of integer vectors representing the variables in each term |

`coeffs,coeffs1,coeffs2` |
Numeric vector representing the coefficients of each word |

The function `Ops.freealg()`

passes binary arithmetic operators
(“`+`

”, “`-`

”, “`*`

”,
“`^`

”, and “`==`

”) to the appropriate
specialist function.

The caret, as in `a^n`

, denotes arithmetic exponentiation, as in
`x^3==x*x*x`

.

Functions `lowlevel_foo()`

are low-level functions that interface
directly with the `C`

routines in the `src/`

directory and
are not intended for the end-user.

Robin K. S. Hankin

1 2 3 4 5 6 7 | ```
rfalg()
as.freealg("1+x+xy+yx") # variables are non-commutative
as.freealg("x") * as.freealg("X") # upper-case letters are lower-case inverses
constant(as.freealg("x+y+X+Y")^6) # OEIS sequence A035610
``` |

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