Order of operations is incorrect for exponents and parentheses

[Jessica Leigh Miller]

When using both parenteses and exponents, the calculator does not always follow standard order of operations.

Order of operations:
1) Parentheses - simplify anything possible within grouping symbols
2) Exponents - unless grouping symbols are used, only the number directly following the carat should be treated as an exponent.
3) Multiplication or Division - whichever occurs first when reading from left to right. Parentheses are a mathematically accepted way of representing multiplication.
4) Addition or Subtraction - whichever occurs first when reading from left to right.

Ex: 3^2*7 yields 63, yet 3^2(7) yields 4782969. Both * and ( ) are acceptable mathematical tools for multiplication, so they should not give two different results.

Ex: 250000000(1.01)^20 gives an inaccurate answer. Order of operations is invalid. The calculator multiplies the 250000000 by the 1.01 before utilizing the exponent. Exponents come before multiplying, and thus 1.01 should be raised to the 20th power before multiplying by 250000000.

Ex: 3^2pi should yield 9pi because exponents trump multiplication. However, the calculator treats this as 3^(2pi), and yields 995.041644893

ProblemType: Bug
DistroRelease: Ubuntu 12.04
Package: gcalctool 6.4.1.1-0ubuntu3
ProcVersionSignature: Ubuntu 3.2.0-39.62-generic 3.2.39
Uname: Linux 3.2.0-39-generic x86_64
NonfreeKernelModules: openafs
ApportVersion: 2.0.1-0ubuntu17.1
Architecture: amd64
Date: Thu Mar 28 19:57:12 2013
MarkForUpload: True
ProcEnviron:
 LANGUAGE=en_US.UTF-8
 PATH=(custom, no user)
 LANG=en_US.UTF-8
 SHELL=/bin/bash
SourcePackage: gcalctool
UpgradeStatus: Upgraded to precise on 2012-12-23 (95 days ago)

[madbiologist (me-again)]

AFAIK and IIRC, parentheses are not the equivalent of a multiplication symbol. It is simply mathematical conventiont to omit the multiplication symbol between two variables, between a constant and a variable, and between a constant or variable and an operator such as ( or Σ.

Note that your first two examples are resolved if you stop using parentheses where they are unnecessary.

The fundamental issue here is the ambiguity caused by a lack of superscript. I've attached an example of what I'm talking about.

[madbiologist (me-again)]

Also see the first, second and fourth paragraphs of https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

[madbiologist (me-again)]

Upon further reading, it seems your third example is valid. One must use parentheses if the entire exponent is 2π, as in 3^(2pi), otherwise 3^2pi should evaluate to 9pi as you said.

Also from the same further reading, using your second example, if not wanting to simply write/enter 250000000*1.01^20 we should use (250000000)(1.01)^20.

[madbiologist (me-again)]

The gcalctool in Ubuntu 12.04 "Precise Pangolin" is a transitional package for the GNOME desktop calculator. In Ubuntu 14.04 "Trusty Tahr" and later, GNOME desktop calculator is called gnome-calculator. gnome-calculator 1:3.10.3-0ubuntu0.1.1 in Ubuntu 14.04 "Trusty Tahr" evaluates all of your examples as you expect it to.