Expression of type Conditional ¶

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, i, j, k, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Exp, Integer, Interval, LessEq, Sum, frac, one, subtract

# build up the expression from sub-expressions
expr = Conditional(Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(j, k)), frac(subtract(Exp(x, j), Exp(x, Add(k, one))), subtract(one, x))), And(InSet(j, Integer), InSet(k, Integer), LessEq(j, k)))

# 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\{\left(\sum_{i = j}^{k} x^{i}\right) = \frac{x^{j} - x^{k + 1}}{1 - x} \textrm{ if } j \in \mathbb{Z} ,  k \in \mathbb{Z} ,  j \leq k\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶