Introduction to the Tolerances Package - Maple Programming Help

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Introduction to the Tolerances Package

 

Calling Sequence

Description

Usage

Entering Tolerances

Computing with Tolerances

Displaying Tolerances

Nominal Value and Tolerance Value

Tolerances and Units

Calling Sequence

with(Tolerances)

Description

• 

The Tolerances package provides an environment to perform computations with quantities involving tolerances.

Usage

• 

After issuing the with(Tolerances) command, quantities involving tolerances can now be entered using a natural notation and any computations involving such quantities will return a value with the associated tolerance result.

• 

The Tolerances package uses interval arithmetic to perform its computations.

Entering Tolerances

• 

Tolerances are entered by specifying the value, followed by the (absolute) tolerance, separated by a plus/minus (±) sign. To enter a plus/minus sign:

– 

Use the palettes. See View>Palettes>Arrange Palettes. (Standard Worksheet interface only)

– 

Use symbol completion.  Enter plusmn, and then press Esc. (Standard Worksheet interface 2-D input only)  For more information, see symbol completion.

– 

Enter &+-.

with(Tolerances):

a := 2 &+- 0.1;

a2.00 ± 0.100

(1)

r := (Pi/2) &+- 0.2;

r1.57 ± 0.200

(2)
  

Note: The plus/minus operator takes precedence over most operators, like ^ and *. As a result, parentheses are required around any non-atomic expression for a nominal value or a tolerance value. For more information, see operators/precedence.

Computing with Tolerances

• 

In addition to simple arithmetic, the following functions can be used with Tolerances:

sin

cos

tan

cot

csc

sec

arcsin

arccos

arctan

arccot

arccsc

arcsec

sinh

cosh

coth

tanh

csch

sech

arcsinh

arccosh

arccoth

arctanh

arccsch

arcsech

abs

sqrt

exp

ln

Ei

 

FresnelC

FresnelS

GAMMA

Psi

LambertW

Zeta

dilog

erf

erfc

 

 

 

with(Tolerances):

a := 2 &+- 0.1;

a2.00 ± 0.100

(3)

b := 3 &+- 0.05;

b3.00 ± 0.0500

(4)

a+b;

5.00 ± 0.150

(5)

a*b;

6.00 ± 0.400

(6)

a^b;

8.13 ± 1.48

(7)

sin(a);

0.905 ± 0.0415

(8)

exp(1/b);

1.40 ± 0.00776

(9)

Displaying Tolerances

  

By default, the Tolerances package displays values with 3 digits even though computations are always performed at the precision indicated by the Digits variable.  Use interface(displayprecision) to control the number of displayed digits.

interface(displayprecision=10);

1

(10)

a := (1/3) &+- 0.1;

a0.3333333332 ± 0.1000000000

(11)

interface(displayprecision=3);

10

(12)

a := (1/3) &+- 0.1;

a0.333 ± 0.100

(13)

Nominal Value and Tolerance Value

• 

The NominalValue command computes the nominal value of a quantity with a tolerance. The nominal value is the center of the confidence interval.

• 

The ToleranceValue command computes the tolerance value of a quantity with a tolerance.  The tolerance is the width of the confidence interval divided by two.

a := 2 &+- 0.1;

a2.000 ± 0.100

(14)

b := 3 &+- 0.05;

b3.000 ± 0.050

(15)

a+b;

5.000 ± 0.150

(16)

NominalValue(a+b);

5.000

(17)

ToleranceValue(a+b);

0.150

(18)

Tolerances and Units

• 

Tolerances and Units can be used together in the same computation

with(Units):

a := 150 &+- 10 * Unit(m);

a150.000 ± 10.000m

(19)

b := 0.2 &+- 0.001 * Unit(km);

b0.200 ± 0.001km

(20)

C := 2*a+2*b;

C700.000 ± 22.000m

(21)

A := a*b;

A30000.000 ± 2150.000m2

(22)

See Also

evalr

operators/precedence

ScientificErrorAnalysis

Units

 


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