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Expression of type Add

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.numbers import Add, Exp, Mult, Neg, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _n, _t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = subtract(Exp(two, subtract(_t, _n)), one)
expr = Add(one, Neg(frac(one, Mult(two, sub_expr1))), Neg(frac(one, Mult(four, Exp(sub_expr1, two)))))
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())
1 - \frac{1}{2 \cdot \left(2^{t - n} - 1\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}
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.()()('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',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 29
operands: 1
1ExprTuple28, 2, 3
2Operationoperator: 33
operand: 6
3Operationoperator: 33
operand: 7
4ExprTuple6
5ExprTuple7
6Operationoperator: 9
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple28, 11
9Literal
10ExprTuple28, 12
11Operationoperator: 14
operands: 13
12Operationoperator: 14
operands: 15
13ExprTuple26, 19
14Literal
15ExprTuple16, 17
16Literal
17Operationoperator: 23
operands: 18
18ExprTuple19, 26
19Operationoperator: 29
operands: 20
20ExprTuple21, 22
21Operationoperator: 23
operands: 24
22Operationoperator: 33
operand: 28
23Literal
24ExprTuple26, 27
25ExprTuple28
26Literal
27Operationoperator: 29
operands: 30
28Literal
29Literal
30ExprTuple31, 32
31Literal
32Operationoperator: 33
operand: 35
33Literal
34ExprTuple35
35Literal