LongAlgebra
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package std
An idempotent function that ensures an object has a non-negative sign.
An idempotent function that ensures an object has a non-negative sign.
Rounds a the nearest integer that is greater than or equal to a.
Rounds a the nearest integer that is greater than or equal to a.
Returns true if x and y are equivalent, false otherwise.
Returns true if x and y are equivalent, false otherwise.
Rounds a the nearest integer that is less than or equal to a.
Rounds a the nearest integer that is less than or equal to a.
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.
Returns true iff a is a an integer.
Returns true iff a is a an integer.
Tests if a is zero.
Tests if a is zero.
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.
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 multiplied with itself n times.
Return a multiplied with itself n times.
Defines an ordering on A where all arrows switch direction.
Defines an ordering on A where all arrows switch direction.
Rounds a to the nearest integer.
Rounds a to the nearest integer.
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.
Approximates a as a Double.
Approximates a as a Double.
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