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How to store mathematical formula in MS SQL Server DB and interpret it using JAVA?

I have to give the user the option to enter in a text field a mathematical formula and then save it in the DB as a String. That is easy enough, but I also need to retrieve it and use it to do calculations.
For example, assume I allow someone to specify the formula of employee salary calculation which I must save in String format in the DB.
GROSS_PAY = BASIC_SALARY - NO_PAY + TOTAL_OT + ALLOWANCE_TOTAL
Assume that terms such as GROSS_PAY, BASIC_SALARY are known to us and we can make out what they evaluate to. The real issue is we can't predict which combinations of such terms (e.g. GROSS_PAY etc.) and other mathematical operators the user may choose to enter (not just the +, -, ×, / but also the radical sigh - indicating roots - and powers etc. etc.). So how do we interpret this formula in string format once where have retrieved it from DB, so we can do calculations based on the composition of the formula.

Building an expression evaluator is actually fairly easy.
See my SO answer on how to write a parser. With a BNF for the range of expression operators and operands you exactly want, you can follow this process to build a parser for exactly those expressions, directly in Java.
The answer links to a second answer that discusses how to evaluate the expression as you parse it.
So, you read the string from the database, collect the set of possible variables that can occur in the expression, and then parse/evaluate the string. If you don't know the variables in advance (seems like you must), you can parse the expression twice, the first time just to get the variable names.

as of Evaluating a math expression given in string form there is a JavaScript Engine in Java which can execute a String functionality with operators.
Hope this helps.

You could build a string representation of a class that effectively wraps your expression and compile it using the system JavaCompiler — it requires a file system. You can evaluate strings directly using javaScript or groovy. In each case, you need to figure out a way to bind variables. One approach would be to use regex to find and replace known variable names with a call to a binding function:
getValue("BASIC_SALARY") - getValue("NO_PAY") + getValue("TOTAL_OT") + getValue("ALLOWANCE_TOTAL")
or
getBASIC_SALARY() - getNO_PAY() + getTOTAL_OT() + getALLOWANCE_TOTAL()
This approach, however, exposes you to all kinds of injection type security bugs; so, it would not be appropriate if security was required. The approach is also weak when it comes to error diagnostics. How will you tell the user why their expression is broken?
An alternative is to use something like ANTLR to generate a parser in java. It's not too hard and there are a lot of examples. This approach will provide both security (users can't inject malicious code because it won't parse) and diagnostics.

What language is this (think it's Java?), and how do I test (using a browser ide) the math is correct in it?

div(1, sum(1, exp(sum(div(5, product(100, .1)), -5))))
I'm using this in a Solr query, and want to verify that it is the same as :
Where x is 5.
Is this language Java?
If it is, why am I getting this output here:
http://ideone.com/LWYWtU
If it isn't, what language is this and how do I test it?
Thanks in advance for your help.
EDIT: To add more of the surrounding code, here is the full boost value I'm sending to Solr:
if(exists(query({!frange l=0 u=60 v=product(geodist(),0.621371)})),div(1, sum(1, exp(sum(div(product(5), product(100, .1)), -5)))),0)
The reason I think it might be Java is because in the docs, it says Most Java Math functions are now supported, including: and then lists the math functions I ended up using for code.

Solr is Java, but that's not relevant since this is a set of functions that Solr parses and evaluate itself (and not related to Java, except that the backing functions are implemented in Java).
As far as I can say from what you've mapped the functions correctly, as long as the 5 in product(5) is the same as X. You shouldn't need product there, as the value can be included in div directly as far as I can see.
A way to validate it would be to use debugQuery in Solr and see what the value is evaluated as, and then compare it to your own value. Remember that floating point evaluation can introduce a few uncertanities.

using java for replacing text in database

i am using replace method for editing text in mysql database and its working well for
every time i try to replace a string by some other string e.g
REPLACE(Eligibility_Points , '(ii)', 'second point is')";
works well for above case
but does not work well in the following case
REPLACE(Eligibility_Points , '(ii)-(iii)', 'second and third point is')";
how should i fix this problem, thanks for your help

Assuming that this is the MySQL REPLACE string function you are talking about, the only reason I can see why the second example wouldn't work is that (maybe) the Eligibility_Points field (or whatever) doesn't contain the first string at all.
Maybe you could provide more context; e.g. what evidence you have that the replace isn't working.
However #vadchen makes a good point. If you do the replacement in the first example, then it will remove all examples that might trigger a replacement in the second example. Maybe you just need to do the "edits" in the reverse order.
There is no need to escape any of the characters in those fragments, either from the Java or SQL perspective.

Java API for plural forms of English words

Are there any Java API(s) which will provide plural form of English words (e.g. cacti for cactus)?

Check Evo Inflector which implements English pluralization algorithm based on Damian Conway paper "An Algorithmic Approach to English Pluralization".
The library is tested against data from Wiktionary and reports 100% success rate for 1000 most used English words and 70% success rate for all the words listed in Wiktionary.
If you want even more accuracy you can take Wiktionary dump and parse it to create the database of singular to plural mappings. Take into account that due to the open nature of Wiktionary some data there might by incorrect.
Example Usage:
English.plural("Facility", 1)); // == "Facility"
English.plural("Facility", 2)); // == "Facilities"

jibx-tools provides a convenient pluralizer/depluralizer.
Groovy test:
NameConverter nameTools = new DefaultNameConverter();
assert nameTools.depluralize("apples") == "apple"
nameTools.pluralize("apple") == "apples"

I know there is simple pluralize() function in Ruby on Rails, maybe you could get that through JRuby. The problem really isn't easy, I saw pages of rules on how to pluralize and it wasn't even complete. Some rules are not algorithmic - they depend on stem origin etc. which isn't easily obtained. So you have to decide how perfect you want to be.

considering java, have a look at modeshapes Inflector-Class as member of the package org.modeshape.common.text. Or google for "inflector" and "randall hauch".

Its hard to find this kind of API. rather you need to find out some websservice which can serve your purpose. Check this. I am not sure if this can help you..
(I tried to put word cacti and got cactus somewhere in the response).

If you can harness javascript, I created a lightweight (7.19 KB) javascript for this. Or you could port my script over to Java. Very easy to use:
pluralizer.run('goose') --> 'geese'
pluralizer.run('deer') --> 'deer'
pluralizer.run('can') --> 'cans'
https://github.com/rhroyston/pluralizer-js
BTW: It looks like cacti to cactus is a super special conversion (most ppl are going to say '1 cactus' anyway). Easy to add that if you want to. The source code is easy to read / update.

Wolfram|Alpha return a list of inflection forms for a given word.
See this as an example:
http://www.wolframalpha.com/input/?i=word+cactus+inflected+forms
And here is their API:
http://products.wolframalpha.com/api/

In JDBC, why do parameter indexes for prepared statements begin at 1 instead of 0?

Everywhere else in Java, anything with an index starts at 0. Is there a reason for the change here or is this just bad design?

Historically, databases have used 1-based indexing for bound parameters. This probably reflects the origins of relational databases in set theory and mathematics, which index elements starting with one, and use zero to represent a null or empty set.
In shell scripts and regular expressions, the zero index usually means something "special". For example, in the case of shell scripts, the zeroth "argument" is actually the command that was invoked.
The choice for JDBC was deliberate but, ultimately, probably causes more confusion and difficulty than it solves.

This was part of a plot by the original language designers to weed out the weak. In the original spec, arrays were numbered from -1, and lists with 1 element returned length =0.
Today, only the java Calendar API remains from this diabolical plot.

Personally I would chalk this up to bad design.

I understand both JDBC and ODBC are based upon the X/Open Call Level Interface. So, it's pre-Java history, like 0-based month numbers.

Likely it's that JDBC was modeled on ODBC.

More human friendly maybe? Also, Java's regular expression Matcher's group starts with 1 as the first matched group.