AlgebraicAlgebra
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package math
An idempotent function that ensures an object has a non-negative sign.
An idempotent function that ensures an object has a non-negative sign.
Returns true if x and y are equivalent, false otherwise.
Returns true if x and y are equivalent, false otherwise.
This is implemented in terms of basic Field ops.
This is implemented in terms of basic Field ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method is overriden.
This is possible because a Double is a rational number.
Defined to be equivalent to additive.sumn(one, n).
Defined to be equivalent to additive.sumn(one, n). That is, n
repeated summations of this ring's one, or -one if n is
negative.
Tests if a is zero.
Tests if a is zero.
Returns false if x and y are equivalent, true otherwise.
Returns false if x and y are equivalent, true otherwise.
Defines an order on B by mapping B to A using f and using As
order to order B.
Defines an order on B by mapping B to A using f and using As
order to order B.
Result of comparing x with y.
Result of comparing x with y. Returns NaN if operands
are not comparable. If operands are comparable, returns a
Double whose sign is:
- negative iff x < y
- zero iff x === y
- positive iff x > y
Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.
Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.
Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.
Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.
This is similar to Semigroup#pow, except that a pow 0 is defined to be
the multiplicative identity.
Given a sequence of as, sum them using the monoid and return the total.
Given a sequence of as, sum them using the monoid and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
If the sequence is empty, returns None. Otherwise, returns Some(total).
Return a multiplicated with itself n times.
Return a multiplicated with itself n times.
Defines an ordering on A where all arrows switch direction.
Defines an ordering on A where all arrows switch direction.
Returns Zero if a is 0, Positive if a is positive, and Negative is a is negative.
Returns Zero if a is 0, Positive if a is positive, and Negative is a is negative.
Returns 0 if a is 0, > 0 if a is positive, and < 0 is a is negative.
Returns 0 if a is 0, > 0 if a is positive, and < 0 is a is negative.
Given a sequence of as, sum them using the monoid and return the total.
Given a sequence of as, sum them using the monoid and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
If the sequence is empty, returns None. Otherwise, returns Some(total).
Return a added with itself n times.
Return a added with itself n times.
Result of comparing x with y.
Result of comparing x with y. Returns None if operands
are not comparable. If operands are comparable, returns Some[Int]
where the Int sign is:
- negative iff x < y
- zero iff x == y
- positive iff x > y