I have a custom calendar, with different months and rules. Can I code for a program which switches between Gregorian calendar and my calendar?

These are the rules to my calendar...

Thirteen Months:

-Alpha (30 Days)

-Beta (30)

-Gamma (30)

-Delta (30)

-Epsilon (30)

-Zeta (30)

-Eta (30)

-Theta (30)

-Iota (30)

-Kappa (30)

-Lambda (30)

-Mu (30 Days)

-Epipleon (Either 5 or 6 Days)

Epipleon has six days IF: A) The Year is divisible by 86400, or B) The Year is divisible by 4, but not by 128

Alpha 1st Year 0 is equivalent to the Gregorian Date December 18th, 1878.

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Can anyone help me embed a widget into a website which will allow for me to toggle between the Gregorian Calendar and my New Calendar? Thanks so much.