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[1

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\OT1/cmr/bx/n/12 Corollary 1.2. []\OT1/cmr/m/it/12 If $\OML/cmm/m/it/12 I$ \OT1
/cmr/m/it/12 is a frac-tional ideal of $\OMS/cmsy/m/n/12 O[]$ \OT1/cmr/m/it/12 
then there ex-ists prime ide-als $[]\U/euf/m/n/12 p[]\OML/cmm/m/it/12 ; [] ; \U
/euf/m/n/12 p[]$
 []

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[]\OT1/cmr/m/n/12 This sec-tion is a first in-tro-duc-tion to MAGMA for al-ge-b
raic num-ber the-ory. MAGMA
 []


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\OT1/cmr/m/n/12 pu-ta-tions. You can use it via the web page []\OT1/cmtt/m/n/12
 http://modular.fas.harvard.edu/calc\OT1/cmr/m/n/12 .
 []

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[]\OT1/cmtt/m/n/12 > K<a> := NumberField(x^3-2);   // a is the image of x in Q[
x]/(x^3-2)[] 
 []

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[][]\OT1/cmtt/m/n/12 > procedure ints(f)   // (procedures don't return anything
; functions do)[] 
 []

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[]    \OT1/cmtt/m/n/12 7*a^10 + 4*a^9 + 4*a^8 + a^7 + a^6 + 4*a^5 + 4*a^3 + 5*a
^2 +  4*a,[] 
 []

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