Expression of type Lambda ¶

from the theory of proveit.numbers.summation ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, i, n, x
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Interval, Natural, Sum, frac, one, subtract, zero

# build up the expression from sub-expressions
expr = Lambda([x, n], Conditional(Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, n)), frac(subtract(one, Exp(x, Add(n, one))), subtract(one, x))), And(InSet(x, Complex), InSet(n, Natural), NotEquals(x, one))))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(x, n\right) \mapsto \left\{\left(\sum_{i = 0}^{n} x^{i}\right) = \frac{1 - x^{n + 1}}{1 - x} \textrm{ if } x \in \mathbb{C} ,  n \in \mathbb{N} ,  x \neq 1\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 1 body: 2
1	ExprTuple	49, 53
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 14 operand: 22
10	Operation	operator: 16 operands: 17
11	Operation	operator: 36 operands: 18
12	Operation	operator: 36 operands: 19
13	Operation	operator: 20 operands: 21
14	Literal
15	ExprTuple	22
16	Literal
17	ExprTuple	23, 24
18	ExprTuple	49, 25
19	ExprTuple	53, 26
20	Literal
21	ExprTuple	49, 54
22	Lambda	parameter: 41 body: 28
23	Operation	operator: 51 operands: 29
24	Operation	operator: 51 operands: 30
25	Literal
26	Literal
27	ExprTuple	41
28	Conditional	value: 31 condition: 32
29	ExprTuple	54, 33
30	ExprTuple	54, 34
31	Operation	operator: 46 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 39 operand: 43
34	Operation	operator: 39 operand: 49
35	ExprTuple	49, 41
36	Literal
37	ExprTuple	41, 42
38	ExprTuple	43
39	Literal
40	ExprTuple	49
41	Variable
42	Operation	operator: 44 operands: 45
43	Operation	operator: 46 operands: 47
44	Literal
45	ExprTuple	48, 53
46	Literal
47	ExprTuple	49, 50
48	Literal
49	Variable
50	Operation	operator: 51 operands: 52
51	Literal
52	ExprTuple	53, 54
53	Variable
54	Literal

Expression of type Lambda¶

from the theory of proveit.numbers.summation¶

Expression of type Lambda ¶

from the theory of proveit.numbers.summation ¶