logo

Expression of type Equals

from the theory of proveit.physics.quantum.QPE

In [1]:
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 e, l
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = frac(one, Exp(e, two))
sub_expr2 = Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))
expr = Equals(Add(sub_expr2, sub_expr1, sub_expr2), Add(sub_expr2, sub_expr2, sub_expr1)).with_wrapping_at(2)
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\begin{array}{c} \begin{array}{l} \left(\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \frac{1}{e^{2}} + \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) =  \\ \left(\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \frac{1}{e^{2}}\right) \end{array} \end{array}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()(2)('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 39
operands: 5
4Operationoperator: 39
operands: 6
5ExprTuple7, 8, 7
6ExprTuple7, 7, 8
7Operationoperator: 9
operand: 12
8Operationoperator: 19
operands: 11
9Literal
10ExprTuple12
11ExprTuple45, 13
12Lambdaparameter: 28
body: 15
13Operationoperator: 35
operands: 16
14ExprTuple28
15Conditionalvalue: 17
condition: 18
16ExprTuple33, 37
17Operationoperator: 19
operands: 20
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple45, 23
21Literal
22ExprTuple28, 24
23Operationoperator: 35
operands: 25
24Operationoperator: 26
operands: 27
25ExprTuple28, 37
26Literal
27ExprTuple29, 30
28Variable
29Operationoperator: 39
operands: 31
30Operationoperator: 39
operands: 32
31ExprTuple33, 45
32ExprTuple34, 42
33Variable
34Operationoperator: 35
operands: 36
35Literal
36ExprTuple37, 38
37Literal
38Operationoperator: 39
operands: 40
39Literal
40ExprTuple41, 42
41Literal
42Operationoperator: 43
operand: 45
43Literal
44ExprTuple45
45Literal