Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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 ExprTuple, Variable
from proveit.numbers import Add, Exp, Mult, Neg, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _eps, _n, _t

# build up the expression from sub-expressions
sub_expr1 = subtract(Exp(two, subtract(_t, _n)), one)
expr = ExprTuple(Add(one, Neg(Variable("_a", latex_format = r"{_{-}a}")), Neg(frac(one, Exp(Add(two, frac(one, _eps)), two)))), Add(one, Neg(frac(one, Mult(two, sub_expr1))), Neg(frac(one, Mult(four, Exp(sub_expr1, two))))))

expr:

# 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(1 - {_{-}a} - \frac{1}{\left(2 + \frac{1}{\epsilon}\right)^{2}}, 1 - \frac{1}{2 \cdot \left(2^{t - n} - 1\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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