Add()

Add the given number to this one (mutating). For a copy, use Added.

also: plus sum increase increment

The forms of this verb

Add · Added

Basic examples (2)

Softanza

oS = StzNumberQ("0.1")
oS.Add("0.2")
? oS.Content()
? oS.IsExact()
? oS.Representation()

Output

0.3
1
decimal

run on 2026-10-02 04:25 inside the library at commit 0e72e2e2c; taken from 07-a-number-that-says-why.en.md(opens in a new tab)

Softanza

oB = StzNumberQ("9007199254740993")
? oB.Representation()
oB.Add(1)
? oB.Content()
? 9007199254740993 + 1

Output

biginteger
9007199254740994
9007199254740992.00

run on 2026-10-02 04:25 inside the library at commit 0e72e2e2c; taken from 07-a-number-that-says-why.en.md(opens in a new tab)

Scope (8)

Softanza

oQ = StzNumberQ("1/3")
? oQ.Representation()
? oQ.IsExact()
oQ.Add("2/3")
? oQ.Content()
? oQ.Same(1)

Output

rational
1
1
1

run on 2026-10-02 04:25 inside the library at commit 0e72e2e2c; taken from 07-a-number-that-says-why.en.md(opens in a new tab)

Softanza

oMix = new stzNumber("1/4")
oMix.Add("0.25")
# a quarter plus 0.25 is a half
? oMix.Content()
# ...as a fraction, not 0.5
? oMix.Representation()
# ...and exactly
? oMix.IsExact()
# ...which is what lets a third survive meeting a decimal
? (new stzNumber("1/3")).AddQ("0.5").Content()

Output

1/2
rational
1
5/6

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_rationals_narrated.ring(opens in a new tab)

Softanza

# 2^53 + 1 is 9007199254740993
? (new stzNumber("9007199254740992")).AddQ(1).Content()
# a 32-digit integer gains one correctly
? (new stzNumber("99999999999999999999999999999999")).AddQ(1).Content()
# 999999999 squared is exact
? (new stzNumber("999999999")).MultiplyByQ("999999999").Content()
# a 20-digit product keeps all 40 digits
? (new stzNumber("12345678901234567890")).MultiplyByQ("98765432109876543210").Content()
# small integer arithmetic is untouched
? (new stzNumber("2")).MultiplyByQ("2").Content()

Output

9007199254740993
100000000000000000000000000000000
999999998000000001
1219326311370217952237463801111263526900
4

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_exactness_narrated.ring(opens in a new tab)

Softanza

oBig = new stzNumber("1/99999999999999999999999999999999")
# a 32-digit denominator survives construction
? oBig.Content()
# ...and reports as a fraction
? oBig.Representation()
oSum = new stzNumber("1/99999999999999999999999999999999")
oSum.Add("1/99999999999999999999999999999999")
# adding it to itself doubles the numerator
? oSum.Content()
# ...exactly
? oSum.IsExact()
# a fraction that reduces from big parts still lands on the small answer
? (new stzNumber("123456789012345678901234567890/246913578024691357802469135780")).Content()

Output

1/99999999999999999999999999999999
rational
2/99999999999999999999999999999999
1
1/2

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_rationals_narrated.ring(opens in a new tab)

Softanza

oHalf = new stzNumber("1/2")
# a half is 0.5
? oHalf.Same("0.5")
# ...whether written as a string or a number
? oHalf.Same(0.5)
# ...and equals another spelling of itself
? oHalf.Same("2/4")
# ...and is not 0.6
? oHalf.Same("0.6")
# a third is NOT 0.333
? (new stzNumber("1/3")).Same("0.333")
# ...nor 0.3333333333
? (new stzNumber("1/3")).Same("0.3333333333")
# a whole number reached through fractions compares equal
? (new stzNumber("2/3")).AddQ("1/3").Same(1)

Output

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_rationals_narrated.ring(opens in a new tab)

Softanza

# an exact product knows it
? (new stzNumber("19.99")).MultiplyByQ("0.15").IsExact()
# ...with nothing to explain
? (new stzNumber("19.99")).MultiplyByQ("0.15").Why()
# a big-integer sum knows it
? (new stzNumber("9007199254740992")).AddQ(1).IsExact()
oSqrt = new stzNumber("2")
oSqrt.SquareRoot()
# a square root does not pretend
? oSqrt.IsExact()
# ...and names the reason
? StzFindFirst("no exact decimal result", oSqrt.Why()) > 0
# IsApproximate is its mirror
? oSqrt.IsApproximate()
# Exactness() reports the register
? oSqrt.Exactness()

Output

1

1
0
1
1
inexact

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_exactness_narrated.ring(opens in a new tab)

Softanza

# 0.1 + 0.2 is 0.3
? (new stzNumber("0.1")).AddQ("0.2").Content()
# 0.1 * 0.1 is 0.01, not 0.0
? (new stzNumber("0.1")).MultiplyByQ("0.1").Content()
# 0.5 * 0.5 is 0.25, not 0.3
? (new stzNumber("0.5")).MultiplyByQ("0.5").Content()
# a price times a rate keeps its cents
? (new stzNumber("19.99")).MultiplyByQ("0.15").Content()
# ...and times a whole number
? (new stzNumber("19.99")).MultiplyByQ(3).Content()
# 0.25 * 0.25 is 0.0625
? (new stzNumber("0.25")).MultiplyByQ("0.25").Content()
# 0.01 * 0.01 is 0.0001
? (new stzNumber("0.01")).MultiplyByQ("0.01").Content()
# 1 + 0.001 is 1.001, not 1.00
? (new stzNumber("1")).AddQ("0.001").Content()
# 0.5 + 0.125 is 0.625, not 0.6
? (new stzNumber("0.5")).AddQ("0.125").Content()
# 10 - 0.001 is 9.999, not 10.00
? (new stzNumber("10")).SubtractQ("0.001").Content()

Output

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_exactness_narrated.ring(opens in a new tab)

Softanza

oThird = new stzNumber("1/3")
oThird.Add("2/3")
# a third plus two thirds is ONE
? oThird.Content()
# ...exactly
? oThird.IsExact()
# ...and equals the number 1
? oThird.Same(1)
# a third plus a sixth
? (new stzNumber("1/3")).AddQ("1/6").Content()
# a half less a third
? (new stzNumber("1/2")).SubtractQ("1/3").Content()
# two thirds of three quarters
? (new stzNumber("2/3")).MultiplyByQ("3/4").Content()
# a half divided by a quarter is two
? (new stzNumber("1/2")).DivideQ("1/4").Content()
# every one of those is exact
? (new stzNumber("2/3")).MultiplyByQ("3/4").IsExact()
# a third times three is one
? (new stzNumber("1/3")).MultiplyByQ(3).Content()
# ...and adding zero changes nothing
? (new stzNumber("1/3")).AddQ(0).Content()

Output

run on 2026-10-02 04:23 inside the library at commit 0e72e2e2c; taken from numeric_rationals_narrated.ring(opens in a new tab)

and 1 more in the tests

The extensions of this method

Each extension, and whether it exists for this method; an extension that exists combines with the others (FindSTCS).

Extension

Exists

What it adds · The names

yes

does what the method does, then returns the object, so the call can be chained · AddQ, AddManyQ, AddManyXTQ

chains on the next, more specific type of object (the Q ladder)

QQQ

chains on the most specific type of object (the Q ladder)

QRT

returns the result as an object of the requested type

takes a case-sensitivity flag

takes the position to start from (StartingAt)

takes bounds that are included (IncludingBounds)

yes

the extended form: more parameters than the base method · AddManyXT, AddManyXTQ

XTT

yet another extension: a further extended form, after XT

includes the position in what it returns

returns positions as sections, [start, end]

selects by a condition

selects by a condition, with the expressive keywords (@NextItem, @PreviousItem...)

takes a direction, forward or backward (Directional)

takes a function (the condition or the update is given as a function); the forms document also uses F for the future form, which defers the action

Many

yes

works on a collection of items instead of one (the plural form) · AddMany, AddManyQ, AddManyXT, AddManyXTQ

Except

takes exceptions, what to leave out (the exceptional form)

returns the result without duplication

Every example is a test file of the library, run inside the library for this page; only those whose output kept every promise their file wrote are shown.

Add()

The forms of this verb

Basic examples (2)

Scope (8)

The extensions of this method

See also