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# Working with the Hebrew Calendar

## Problem

You need to work with dates in the Hebrew system.

## Solution

You need to build up some basic utilities to work effectively with the Hebrew calendar. Hebrew years have 12 months in a regular year and 13 in a leap year. Leap years occur on the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of the ```Metonic cycle``` (see the “Discussion” section). A concise means of making this determination is given by the relation 7y + 1 mod 19 < 7. From this, you can easily devise a function to determine the last month of any Hebrew year:

```<xsl:template name="date:last-month-of-hebrew-year">
<xsl:param name="year"/>
<xsl:choose>
<xsl:when test="(7 * \$year + 1) mod 19 &lt; 7">
<xsl:value-of select="13"/>
</xsl:when>
<xsl:otherwise>
<xsl:value-of select="12"/>
</xsl:otherwise>
</xsl:choose>
</xsl:template>```

As a prerequisite to determining the number of days in any given month or year, you need to encapsulate the complex rules that determine when the Hebrew new year starts. See the paper by Dershowitz and Reingold for detailed explanation.

```<-- Number of days ellased from the Sunday prior to the start of the Hebrew calender
to the mean conjunction of Tishri of Hebrew `year`. --> <xsl:template name="date:hebrew-calendar-ellapsed-days"> <xsl:param name="year"/> <xsl:variable name="hebrew-leap-year" select="(7 * \$year + 1) mod 19 &lt; 7"/> <xsl:variable name="hebrew-leap-year-last-year" select="(7 * (\$year - 1) + 1) mod 19 &lt; 7"/> <xsl:variable name="months-ellapsed" ...```

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