Mathematical & logical expression parser demo

• Numbers may be integer or fractional. Examples:1, -1.5, .345678.
• Arithmetic operations are + (plus), - (minus), * (times), / (divide), ^ (power), % (modulus). Standard operation precedence applies. Example: 5*3-2^2+1/1 equals 12.
• Use parentheses (x^2)+5. If you open one, make sure to close it. Parentheses may be nested. Example: (5*(3-2^2)+1)/1 equals -4.
• Legal variables are those mentioned in the question. For instance, if the question mentions z, you may write z^2 - 2*z+1.
• You may use implicit multiplication: 3z and 3 z are the same as 3*z. Note that you must put a space if you want to multiply a variable and a number (e.g. z 3 equals 3*z but z3 is intrepreted as a single variable), or a variable and a variable (e.g. x y).
• Except variable multiplication cases explained above, there is no need to put spaces between numbers and operations (e.g. 3--3 equals 6).
• To use functions like sin, tan, log, put parentheses around the argument. For instance, sin(x^2). Functions can be nested: sin(x^2+tan(x)). See the full list of functions.
• You may use mathematical constants like in your expression. See the full list of constants.

You may write a relation whose left-hand-side and right-hand-side are legal expressions (they may contain the same or different variables). Relational operations are = (assignment/equals), != (not assigned/not equals), < (less-than), <= (less-than-or-equals), > (greater-than),>= (greater-than-or-equals).

Anti-Commutative Relations

"Less-" and "greater-" are opposites: x <= y is equivalent to y <= x, while x^2 < x-1 is the same as x-1 > x^2.

Non-Commutative Relations

However, x = 5 is not normally equivalent to 5 = x. Similarly x != 5 is not equivalent to 5 != x. The reason is that "=" is intepreted as assigning the value 5 to the variable x in your expression; 5 is not assigned the value x.

This rule applies except for questions that specifically ask for you to write an equation. In that case, x = 5 is the same as 5 = x and x != 5 is the same as 5 != x.

This advanced mathematical expression parser is the core of RUReady, a free online college readiness self-assessment and learning Web site intended to improve student college readiness. Its most important innovation is the ability to analyze student responses to open-ended math questions during an adaptive learning process, and provide detailed error feedback to the student about the erroneous parts in his/her response. In addition to standard expression matching and determining whether the student's response is mathematically legal, the parser is capable of comparing a reference string provided by instructors with student's response, evaluating whether they are mathematically equivalent expressions, and classifying student's response elements as correct, wrong, unrecognized, missing or redundant. The parsing algorithm is relatively simple and does not rely on complicated symbolic algebra software; yet, it is powerful and accurate by relying on syntax tree pattern matching. The parsing algorithm's accuracy was demonstrated on real-world examples from introductory math college courses.

The parser's grammar rules recognize conventional arithmetic and logical operator precedence and association. They also avoid the problem of left recursion, and their implementation avoids problems with the infinite loop inherent in the cyclic dependencies of the rules. In other words, the rules may look simple, but their structure is subtle. The parser is written in Java(TM) and builds upon a parsing package provided by Steven J. Metsker (version 1.0).

The parser, now available in prototype form, is protected by a Pending U.S. Patent DOCKET NO. 00846 25702.PROV.

If you are a student, skip this section.

You can control the behavior of the parser demo by tuning the flags in the "Parser Options" box on your screen.

• Implicit multiplication: If set, multiplication need not be explicitly specified: 3 z are the same as 3*z. Otherwise, multiplication must be explicitly specified by "*".
• Precision [digits]:: The number of significant digits required to be the same in two expressions to make them equivalent. Must be between 1 and 14 (inclusive).
• Arithmetic mode: The field over which arithmetic takes place. "Integer" means all number operands are rounded to the closest integer during matching. "Rational" means the expression will be rounded to the nearest rational number when evaluated and displayed. "Real" means arithmetic is performed over the real numbers. "Complex" allows complex arithmetic (use i to represent complex unity). Note that sqrt(x^2) and abs(x) are equivalent over the reals, but not over the complex.
• Variable: Note: in the parser demo, the legal variables are x,y,z.

Functions of One Variable

Functions of Two Variables