3.2.USINGTHEMATHLIBRARY 27
>>> 3.0 * 4.0
12.0
>>> 3 * 4
12
>>> 10.0 / 3.0
3.33333333333
>>> 10 / 3
3
>>> 10 % 3
1
abs(5)
5
abs(-3.5)
3.5
Noticehowoperationsonfloatsproducefloats,andoperationsonintsproduceints.Mostofthetime,we
don’t have toworryaboutwhattypeofoperationis beingperformed;forexample,integeradditionproduces
prettymuchthesameresultasfloatingpointaddition.
However, inthecaseofdivision,theresultsarequitedifferent. Integerdivisionalwaysproducesan
integer, discardingany fractionalresult.Thinkofintegerdivisionas“gozinta.” Theexpression,10 / 3
produces3 becausethreegozinta(goesinto)tenthreetimes(witha remainderofone). Thethirdtolast
exampleshowstheremainderoperation(%) inaction.Theremainderofdividing 10 by3 is 1.Thelasttwo
examplesillustratetakingtheabsolutevalueofanexpression.
YoumayrecallfromChapter2 thatSuzieProgrammerusedtheexpression9.0 / 5.0inhertempera-
tureconversionprogramratherthan9 / 5. Now youknow why. Theformergivesthecorrectmultiplierof
1 8, whilethelatteryieldsjust1, since5 gozinta9 justonce.
3.2 UsingtheMathLibrary.
BesidestheoperationslistedinTable3.1,Pythonprovidesmany otherusefulmathematicalfunctionsina
specialmathlibrary. Alibraryisjusta modulethatcontainssomeusefuldefinitions.Ournextprogram
illustratestheuseofthislibrarytocomputetherootsofquadraticequations.
A quadraticequationhastheformax^2 bx c 0.Suchanequationhastwo solutionsforthevalueof
xgivenbythequadraticformula:
x b
b^2 4 ac
2 aLet’s writea programthatcanfindthesolutionstoa quadraticequation.Theinputtotheprogramwillbethe
valuesofthecoefficientsa,b, andc. Theoutputsarethetwo valuesgivenbythequadraticformula.Here’s a
programthatdoesthejob.
quadratic.py
A program thatcomputes the real roots of a quadratic equation.
Illustrates use of the mathlibrary.
Note: this programcrashes if the equation has no real roots.
import math # Makesthe math library available.
def main():
print "This programfinds the real solutions to a quadratic"
print
a, b, c = input("Please enter the coefficients (a, b, c): ")discRoot = math.sqrt(b* b - 4 * a * c)