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|000051d0| 20 24 65 78 70 72 24 20 | 69 73 20 61 20 70 6f 6c | $expr$ |is a pol|
|000051e0| 79 6e 6f 6d 69 61 6c 2c | 20 61 20 70 6f 77 65 72 |ynomial,| a power|
|000051f0| 20 73 65 72 69 65 73 20 | 6f 72 20 61 20 72 61 74 | series |or a rat|
|00005200| 69 6f 6e 61 6c 20 66 75 | 6e 63 74 69 6f 6e 20 77 |ional fu|nction w|
|00005210| 68 6f 73 65 20 6d 61 69 | 6e 0a 76 61 72 69 61 62 |hose mai|n.variab|
|00005220| 6c 65 20 69 73 20 24 58 | 24 2c 20 73 61 79 2c 20 |le is $X|$, say, |
|00005230| 74 68 69 73 20 63 72 65 | 61 74 65 73 0a 61 20 70 |this cre|ates.a p|
|00005240| 6f 77 65 72 20 73 65 72 | 69 65 73 20 28 61 6c 73 |ower ser|ies (als|
|00005250| 6f 20 7a 65 72 6f 29 20 | 6f 66 20 70 72 65 63 69 |o zero) |of preci|
|00005260| 73 69 6f 6e 20 24 76 2a | 6b 24 20 77 68 65 72 65 |sion $v*|k$ where|
|00005270| 20 24 76 24 20 69 73 20 | 74 68 65 0a 24 58 24 2d | $v$ is |the.$X$-|
|00005280| 61 64 69 63 20 76 61 6c | 75 61 74 69 6f 6e 20 6f |adic val|uation o|
|00005290| 66 20 24 65 78 70 72 24 | 20 28 73 65 65 20 32 2e |f $expr$| (see 2.|
|000052a0| 33 2e 36 20 61 6e 64 20 | 32 2e 33 2e 39 2e 29 2e |3.6 and |2.3.9.).|
|000052b0| 0a 0a 4e 6f 74 65 3a 20 | 61 73 20 75 73 75 61 6c |..Note: |as usual|
|000052c0| 2c 20 6c 6f 77 65 72 63 | 61 73 65 20 7b 5c 62 66 |, lowerc|ase {\bf|
|000052d0| 20 6f 7d 20 69 73 20 61 | 6c 6c 6f 77 65 64 2c 20 | o} is a|llowed, |
|000052e0| 62 75 74 20 77 65 20 64 | 6f 20 6e 6f 74 0a 61 64 |but we d|o not.ad|
|000052f0| 76 69 73 65 20 74 6f 20 | 75 73 65 20 69 74 20 73 |vise to |use it s|
|00005300| 69 6e 63 65 20 69 74 20 | 68 61 73 20 61 20 64 69 |ince it |has a di|
|00005310| 66 66 65 72 65 6e 74 20 | 6d 61 74 68 65 6d 61 74 |fferent |mathemat|
|00005320| 69 63 61 6c 20 6d 65 61 | 6e 69 6e 67 2e 0a 0a 5c |ical mea|ning...\|
|00005330| 76 66 69 6c 6c 5c 65 6a | 65 63 74 0a 0a 0a 0a |vfill\ej|ect.... |
+--------+-------------------------+-------------------------+--------+--------+
